SZTE Repository of Papers and Books: No conditions. Results ordered -Date Deposited. 2020-07-11T08:02:42ZEPrintshttp://acta.bibl.u-szeged.hu/images/acta.jpghttp://acta.bibl.u-szeged.hu/2018-11-07T10:51:25Z2018-11-07T14:02:00Zhttp://acta.bibl.u-szeged.hu/id/eprint/55732This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557322018-11-07T10:51:25ZHopf bifurcation analysis of scalar implicit neutral delay differential equationHopf bifurcation analysis is conducted on a scalar implicit Neutral Delay Differential Equation (NDDE) by means of the extension of two analytical methods: 1) center manifold reduction combined with normal form theory; 2) method of multiple scales. The modifications of the classical algorithms originally developed for explicit differential equations lead to the same algebraic results, which are further confirmed by numerical simulations. It is shown that the generalizations of these regular normal form calculation methods are useful for the local nonlinear analysis of implicit NDDEs where the explicit formalism is typically not accessible and the existence and uniqueness of solutions around the equilibrium are only assumed together with the existence of a smooth local center manifold.Li ZhangGábor Stépán2018-11-07T10:40:26Z2018-11-07T14:00:47Zhttp://acta.bibl.u-szeged.hu/id/eprint/55731This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557312018-11-07T10:40:26ZExtensions of Gronwall’s inequality with quadratic growth terms and applicationsWe obtain some new Gronwall type inequalities where, instead of linear growth assumptions, we allow quadratic (or more) growth provided some additional conditions are satisfied. Applications are made to both local and nonlocal boundary value problems for some second order ordinary differential equations which have quadratic growth in the derivative terms.Jeffrey R. L. Webb2018-11-07T10:31:59Z2018-11-07T13:59:09Zhttp://acta.bibl.u-szeged.hu/id/eprint/55730This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557302018-11-07T10:31:59ZMultiple solutions of nonlinear elliptic functional differential equationsWe shall consider weak solutions of boundary value problems for elliptic functional differential equations of the form n j=1 Dj [aj(x, u, Du; u)] + a0(x, u, Du; u) = F, x ∈ Ω with homogeneous boundary conditions, where Ω ⊂ Rn is a bounded domain and ; u denotes nonlocal dependence on u (e.g. integral operators applied to u). By using the theory of pseudomonotone operators, one can prove existence of solutions. However, in certain particular cases it is possible to find theorems on the number of solutions. These statements are based on arguments for fixed points of certain real functions and operators, respectively.László Simon2018-11-07T10:05:21Z2018-11-07T13:57:57Zhttp://acta.bibl.u-szeged.hu/id/eprint/55729This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557292018-11-07T10:05:21ZParametrisation for boundary value problems with transcendental non linearities using polynomial interpolationA constructive technique of analysis involving parametrisation and polynomial interpolation is suggested for general non-local problems for ordinary differential systems with locally Lipschitzian transcendental non-linearities. The practical application of the approach is shown on a numerical example.András RontóMiklós RontóNatalya Shchobak2018-11-07T10:01:01Z2018-11-07T13:56:43Zhttp://acta.bibl.u-szeged.hu/id/eprint/55728This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557282018-11-07T10:01:01ZThe maximum principle with lack of monotonicityWe establish a maximum principle for the weighted (p, q)-Laplacian, which extends the general Pucci–Serrin strong maximum principle to this quasilinear abstract setting. The feature of our main result is that it does not require any monotonicity assumption on the nonlinearity. The proof combines a local analysis with techniques on nonlinear differential equations.Patrizia PucciVicenţiu D. Rădulescu2018-11-07T09:58:13Z2018-11-07T13:55:48Zhttp://acta.bibl.u-szeged.hu/id/eprint/55727This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557272018-11-07T09:58:13ZA Perron type theorem for positive solutions of functional differential equationsA nonlinear perturbation of a linear autonomous retarded functional differential equation is considered. According to a Perron type theorem, with the possible exception of small solutions the Lyapunov exponents of the solutions of the perturbed equation coincide with the real parts of the characteristic roots of the linear part. In this paper, we study those solutions which are positive in the sense that they lie in a given order cone in the phase space. The main result shows that if the Lyapunov exponent of a positive solution of the perturbed equation is finite, then it is a characteristic root of the unperturbed equation with a positive eigenfunction. As a corollary, a necessary and sufficient condition for the existence of a positive solution of a linear autonomous delay differential equation is obtained.Mihály Pituk2018-11-07T09:54:06Z2018-11-07T13:51:02Zhttp://acta.bibl.u-szeged.hu/id/eprint/55726This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557262018-11-07T09:54:06ZSecond order systems with nonlinear nonlocal boundary conditionsThis paper is concerned with the second order differential equation with not necessarily linear nonlocal boundary condition. The existence of solutions is obtained using the properties of the Leray–Schauder degree. The results generalize and improve some known results with linear nonlocal boundary conditions.Jean MawhinBogdan PrzeradzkiKatarzyna Szymańska-Dębowska2018-11-07T09:21:04Z2018-11-07T13:49:32Zhttp://acta.bibl.u-szeged.hu/id/eprint/55725This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557252018-11-07T09:21:04ZOn the uniqueness of limit cycle for certain Liénard systems without symmetryThe problem of the uniqueness of limit cycles for Liénard systems is investigated in connection with the properties of the function F(x). When α and β (α < 0 < β) are the unique nontrivial solutions of the equation F(x) = 0, necessary and sufficient conditions in order that all the possible limit cycles of the system intersect the lines x = α and x = β are given. Therefore, in view of classical results, the limit cycle is unique. Some examples are presented to show the applicability of our results in situations with lack of symmetry.Makoto HayashiGabriele VillariFabio Zanolin2018-11-07T09:16:20Z2018-11-07T13:48:08Zhttp://acta.bibl.u-szeged.hu/id/eprint/55724This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557242018-11-07T09:16:20ZSharp estimation for the solutions of inhomogeneous delay differential and Halanay-type inequalitiesThis paper is devoted to inhomogeneous Halanay-type inequalities together with inhomogeneous linear delay differential inequalities and equations. Based on the the variation of constants formula and some results borrowed from a recent paper of the authors, sharp conditions for the boundedness and the existence of the limit of the nonnegative solutions are established. The sharpness of the results are illustrated by examples and by comparison of results in some earlier works.István GyőriLászló Horváth2018-11-07T08:21:42Z2018-11-07T13:47:08Zhttp://acta.bibl.u-szeged.hu/id/eprint/55723This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557232018-11-07T08:21:42ZPermanence in a class of delay differential equations with mixed monotonicityIn this paper we consider a class of delay differential equations of the form x˙(t) = α(t)h(x(t − τ), x(t − σ)) − β(t)f(x(t)), where h is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity.István GyőriFerenc HartungNahed A. Mohamady2018-11-07T08:15:23Z2018-11-07T13:45:17Zhttp://acta.bibl.u-szeged.hu/id/eprint/55722This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557222018-11-07T08:15:23ZMoving average network examples for asymptotically stable periodic orbits of monotone mapsFor a certain type of discrete-time nonlinear consensus dynamics, asymptotically stable periodic orbits are constructed. Based on a simple ordinal pattern assumption, the Frucht graph, two Petersen septets, hypercubes, a technical class of circulant graphs (containing Paley graphs of prime order), and complete graphs are considered – they are all carrying moving average monotone dynamics admitting asymptotically stable periodic orbits with period 2. Carried by a directed graph with 594 (multiple and multiple loop) edges on 3 vertices, also the existence of asymptotically stable r-periodic orbits, r = 3, 4, . . . is shown.Barnabás M. GarayJudit Várdai2018-11-06T14:54:49Z2018-11-07T13:44:15Zhttp://acta.bibl.u-szeged.hu/id/eprint/55721This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557212018-11-06T14:54:49ZA note on dissipativity and permanence of delay difference equationsÁbel Garab2018-11-06T14:52:24Z2018-11-07T13:42:57Zhttp://acta.bibl.u-szeged.hu/id/eprint/55720This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557202018-11-06T14:52:24ZControllability of strongly degenerate parabolic problems with strongly singular potentialsWe prove a null controllability result for a parabolic Dirichlet problem with non smooth coefficients in presence of strongly singular potentials and a coefficient degenerating at an interior point. We cover the case of weights falling out the class of Muckenhoupt functions, so that no Hardy-type inequality is available; for instance, we can consider Coulomb-type potentials. However, through a cut-off function method, we recover the desired controllability result.Genni FragnelliDimitri Mugnai2018-11-06T14:48:33Z2018-11-07T13:41:50Zhttp://acta.bibl.u-szeged.hu/id/eprint/55719This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557192018-11-06T14:48:33ZPermanence for a class of non-autonomous delay differential systemsWe are concerned with a class of n-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of delay differential equations. Sufficient conditions for the exponential asymptotic stability of the linear system are established. By using this stability, the permanence of the perturbed nonlinear system is studied. Under more restrictive constraints on the coefficients, the system has a cooperative type behaviour, in which case explicit uniform lower and upper bounds for the solutions are obtained. As an illustration, the asymptotic behaviour of a non-autonomous Nicholson system with distributed delays is analysed.Teresa Faria2018-11-06T14:46:23Z2018-11-07T13:37:27Zhttp://acta.bibl.u-szeged.hu/id/eprint/55718This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557182018-11-06T14:46:23ZOperator splitting methods for the Lotka-Volterra equationsGeometric integrators are numerical methods for differential equations that preserve geometric properties. In this article we investigate the questions of constructing such methods for the well-known Lotka–Volterra predator–prey system by using the operator splitting method. We use different numerical methods combined with the operator splitting method and analyse if they preserve the geometric properties of the original system.István FaragóGabriella Svantnerné Sebestyén2018-11-06T14:41:06Z2018-11-07T13:36:06Zhttp://acta.bibl.u-szeged.hu/id/eprint/55717This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557172018-11-06T14:41:06ZLong-time behaviour of solutions of delayed-type linear differential equationsJosef Diblík2018-11-06T14:38:47Z2018-11-07T13:34:36Zhttp://acta.bibl.u-szeged.hu/id/eprint/55716This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557162018-11-06T14:38:47ZSmall solutions of the damped half-linear oscillator with step function coefficientsWe give a sufficient condition guaranteeing the existence of a small solution, that is a non-trivial solution which tends to 0 as t tends to infinity, in the case when both damping and elasticity coefficients are step functions. With our main theorem we not just generalize the corresponding theorem for the linear case n = 1, but we even sharpen Hatvani’s theorem concerning the undamped half-linear differential equation. Keywords: small solution, asymptotic stability, half-linear differential equation, step function coefficients, damping, difference equations.Attila DénesLászló Székely2018-11-06T14:33:48Z2018-11-07T13:33:08Zhttp://acta.bibl.u-szeged.hu/id/eprint/55715This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557152018-11-06T14:33:48ZOn stabilizability of the upper equilibrium of the asymmetrically excited inverted pendulumLászló Csizmadia2018-11-06T14:30:34Z2018-11-07T13:31:53Zhttp://acta.bibl.u-szeged.hu/id/eprint/55714This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557142018-11-06T14:30:34ZPositive kernels, fixed points, and integral equationsTheodore A. BurtonIoannis K. Purnaras2018-11-06T14:23:46Z2018-11-07T13:30:28Zhttp://acta.bibl.u-szeged.hu/id/eprint/55713This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557132018-11-06T14:23:46ZOn the stability properties of a delay differential neoclassical model of economic growthThe main aim of this paper is to establish sharp global stability conditions for the positive equilibrium of a well-known model of economic growth when a delay is considered in the production function. In order to deal with a broad scenario, we establish some results of global attraction for a general family of differential equations with variable delay; for it, we use the notion of strong attractor, which allows us to simplify the proofs, as well as to generalize previous results. Our study reveals that sometimes production delays are not able to destabilize the positive equilibrium, even if they are large. In other cases, the stability properties of the equilibrium depend on the interaction between the delay and other relevant model parameters, leading sometimes to stability windows in the bifurcation diagram.Sebastián Buedo-FernándezEduardo Liz2018-11-06T14:19:52Z2018-11-07T13:29:22Zhttp://acta.bibl.u-szeged.hu/id/eprint/55712This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557122018-11-06T14:19:52ZSimilarity transformation approach for a heated ferrofluid flow in the presence of magnetic fieldThe aim of this paper is to investigate theoretically the magnetothermomechanical interaction between a heated viscous incompressible ferrofluid and a cold wall in the presence of a spatially varying field. Similarity transformation is used to convert the governing non-linear boundary-layer equations into coupled nonlinear ordinary differential equations. These equations are numerically solved using a discretization scheme using higher derivative method (HDM). The effects of governing parameters corresponding to various physical conditions are analyzed. Numerical results are obtained for distributions of velocity and temperature, the dimensionless wall skin friction and heat-transfer coefficients. The results indicate that two solution exists in some cases. A comparison with previous studies available in the literature has been done and we found an excellent agreement with it.Gabriella BognárKrisztián Hriczó2018-11-06T14:15:03Z2018-11-07T13:23:14Zhttp://acta.bibl.u-szeged.hu/id/eprint/55711This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557112018-11-06T14:15:03ZControl of epidemic propagation on networks by using a mean-field modelEpidemic propagation is controlled conventionally by vaccination or by quarantine. These methods have been widely applied for different compartmental ODE models of epidemic propagation. When epidemic spread is considered on a network, then it is natural to control the propagation process by changing the network structure. Namely, SI links, connecting a susceptible individual to an infected one, can be deleted. This would lead to a disconnected network, which is not realistic, hence new SS links can be created in order to keep the network well connected. Thus it seems to be promising to drive the process to a target with no infection and a prescribed average degree by deleting SI links and creating SS links in an appropriate way. It was shown previously that this can be done for the pairwise ODE approximation of SIS epidemic propagation. In this paper this is extended to the original stochastic process by using the control signals computed from the ODE approximation.Ágnes BodóPéter L. Simon2018-11-06T14:07:27Z2018-11-07T13:54:50Zhttp://acta.bibl.u-szeged.hu/id/eprint/55710This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/557102018-11-06T14:07:27ZGlobal stability in a system using echo for position controlWe consider a system of equations describing automatic position control by echo. The system can be reduced to a single differential equation with state-dependent delay. The delayed terms come from the control mechanism and the reaction time. H.-O. Walther [Differ. Integral Equ. 15(2002), No. 8, 923–944] proved that stable periodic motion is possible for large enough reaction time. We show that, for sufficiently small reaction lag, the control is perfect, i.e., the preferred position of the system is globally asymptotically stable.Ferenc A. BarthaTibor Krisztin