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

Iannizzotto Antonio

;Marras Monica;Nikolaos S. Papageorgiou

2018-01-01

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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 con- ditions. 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.