Nonlinear Neumann problems with indefinite potential and concave terms

Abstract

In this paper we conduct a detailed study of Neumann problems driven by a nonhomogeneous differential operator plus an indefinite potential and with concave contribution in the reaction. We deal with both superlinear and sublinear (possibly resonant) problems and we produce constant sign and nodal solutions. We also examine semilinear equations resonant at higher parts of the spectrum and equations with a negative concavity.

Document Type

Article

DOI

https://doi.org/10.3934/cpaa.2015.14.2561

Keywords

bifurcation, local minimizer, nonlinear maximum principle, positive solutions, nodal solutions, harnack inequality, nonlinear regularity

Publication Date

2015

Journal Title

Communications on Pure & Applied Analysis

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