Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 60, pp. 1-15.

Title: Existence and multiplicity for a superlinear elliptic problem under
       a non-quadradicity condition at infinity 
       
Authors: Leandro Recova (T-Mobile Inc., Ontario, CA, USA)
         Adolfo Rumbos (Pomona College, Claremont, CA, USA)

Abstract:
 In this article, we study the existence and multiplicity of solutions of the
 boundary-value problem
 $$\displaylines{
 -\Delta u = f(x,u), \quad \text{in } \Omega, \cr
 u = 0, \quad \text{on } \partial\Omega,
 }$$
 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.