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arXiv · 1801.01868

Multiplicity results and qualitative properties for semilinear elliptic problems with Neumann boundary conditions

Oscar Agudelo·Santiago Correa·Daniel Restrepo·Carlos Velez
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Abstract

In this paper we study multiplicity and qualitative behavior of solutions for semilinear elliptic problems with neumann boundary condition and asymptotically linear smooth nonlinearity. We provide sufficient conditions on the number of eigenvalues the derivative of the nonlinearity crosses to guarantee existence of at least five nontrivial solutions. The techniques we use are a combination of minimization, Leray-Schauder degree, Morse Theory and Reduction method a la Castro-Lazer.

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Oscar Agudelo, Santiago Correa, Daniel Restrepo, Carlos Velez. 2018-01-05. Multiplicity results and qualitative properties for semilinear elliptic problems with Neumann boundary conditions. https://arxiv.org/abs/1801.01868

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