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

• Main Authors: Leandro Recova, Adolfo Rumbos
• Format: Article
• Language: English
• Published: Texas State University 2020-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: semilinear elliptic boundary value problem; superlinear subcritical growth; infinite dimensional morse theory; critical groups
• Online Access: http://ejde.math.txstate.edu/Volumes/2020/60/abstr.html

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.