Nodal and multiple solutions for a nonhomogeneous Neumann boundary problem

Liliana Klimczak

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arXiv · 1505.01867

Nodal and multiple solutions for a nonhomogeneous Neumann boundary problem

Liliana Klimczak

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Abstract

We consider a nonlinear Neumann problem driven by a $p$-Laplacian-type, nonhomogeneous elliptic differential operator and a Carath\'eodory reaction term. In this paper we prove the existence of two extremal constant sign smooth solutions and a nontrivial nodal smooth solution. In the proof we use variational methods with truncation techniques, critical point theory and Morse theory (critical groups).

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Liliana Klimczak. 2015-05-07. Nodal and multiple solutions for a nonhomogeneous Neumann boundary problem. https://arxiv.org/abs/1505.01867

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