Leandro Recova, Adolfo Rumbos
In this article, we study the existence and multiplicity of solutions of the boundary-value problem
where denotes the N-dimensional Laplacian, is a bounded domain with smooth boundary, , in , 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  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 |
Ontario, CA 91761, USA
| Adolfo J. Rumbos |
Department of Mathematics
Claremont, CA 91711, USA
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