Multiple solutions of nonlinear elliptic functional differential equations

Simon, László: Multiple solutions of nonlinear elliptic functional differential equations. (2018)

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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: Journal
Publication full: Electronic journal of qualitative theory of differential equations : special edition
Date: 2018
Volume: 3
Number: 60
ISSN: 1417-3875
Page Range: pp. 1-9
Uncontrolled Keywords: Differenciálegyenlet - nemlineáris, Differenciálegyenlet - elliptikus
Additional Information: Bibliogr.: 9. p. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 07. 10:31
Last Modified: 2020. Jul. 29. 12:20

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