Electron. J. Differential Equations, Vol. 2020 (2020), No. 60, pp. 1-15.

Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity

Leandro Recova, Adolfo Rumbos

In this article, we study the existence and multiplicity of solutions of the boundary-value problem

where $\Delta$ denotes the N-dimensional Laplacian, $\Omega$ is a bounded domain with smooth boundary, $\partial\Omega$, in $\mathbb{R}^N$ $(N\geq 3)$, and f is a continuous function having subcritical growth in the second variable. Using infinite-dimensional Morse theory, we extended the results of Furtado and Silva [9] by proving the existence of a second nontrivial solution under a non-quadradicity condition at infinity on the non-linearity. Assuming more regularity on the non-linearity f, we are able to prove the existence of at least three nontrivial solutions.

Submitted February 28, 2020. Published June 16, 2020.
Math Subject Classifications: 35J20.
Key Words: Semilinear elliptic boundary value problem; superlinear subcritical growth; infinite dimensional Morse theory; critical groups.

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Leandro L. Recôva
T-Mobile Inc.
Ontario, CA 91761, USA
email: leandro.recova3@t-mobile.com
Adolfo J. Rumbos
Department of Mathematics
Pomona College
Claremont, CA 91711, USA
email: arumbos@pomona.edu

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