Constant sign and nodal solutions for nonhomogeneous Robin boundary value problems with asymmetric reactions

Iannizzotto, Antonio and Marras, Monica and Papageorgiou, Nikolaos S.: Constant sign and nodal solutions for nonhomogeneous Robin boundary value problems with asymmetric reactions. In: Electronic journal of qualitative theory of differential equations 71. pp. 1-28. (2018)

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Abstract

We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric reaction term depending on a positive parameter, coupled with Robin boundary conditions. Under appropriate hypotheses on both the leading differential operator and the reaction, we prove that, if the parameter is small enough, the problem admits at least four nontrivial solutions: two of such solutions are positive, one is negative, and one is sign-changing. Our approach is variational, based on critical point theory, Morse theory, and truncation techniques.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 71
ISSN: 1417-3875
Page Range: pp. 1-28
Uncontrolled Keywords: Differenciálegyenlet - elliptikus, Differenciálegyenlet - nemlineáris, Differenciálegyenlet - határérték probléma
Additional Information: Bibliogr.: p. 26-28. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 07. 11:46
Last Modified: 2018. Nov. 07. 11:46
URI: http://acta.bibl.u-szeged.hu/id/eprint/55741

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