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Constant sign and nodal solutions for nonlinear Robin equations with locally defined source term

    Nikolaos S. Papageorgiou Affiliation
    ; Calogero Vetro Affiliation
    ; Francesca Vetro Affiliation

Abstract

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

Keyword : locally defined reaction, nonlinear regularity, nonlinear maximum principle, constant sign and nodal solutions, critical groups

How to Cite
Papageorgiou, N. S., Vetro, C., & Vetro, F. (2020). Constant sign and nodal solutions for nonlinear Robin equations with locally defined source term. Mathematical Modelling and Analysis, 25(3), 374-390. https://doi.org/10.3846/mma.2020.11031
Published in Issue
May 13, 2020
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