Multiple solutions of nonlinear elliptic functional differential equations

Simon, László: Multiple solutions of nonlinear elliptic functional differential equations. Electronic journal of qualitative theory of differential equations 60. pp. 1-9. (2018)

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Abstract

We 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.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 60
Page Range: pp. 1-9
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2018.1.60
Uncontrolled Keywords: Differenciálegyenlet - nemlineáris, Differenciálegyenlet - elliptikus
Additional Information: Bibliogr.: 9. p. ; összefoglalás angol nyelven
Date Deposited: 2019. May. 30. 16:20
Last Modified: 2019. May. 30. 16:20
URI: http://acta.bibl.u-szeged.hu/id/eprint/58125

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