Abstract
In this paper we establish the existence of multiple solutions for the semilinear elliptic problem \begin{equation}\alignedat 2 -\Delta u&=g(x,u) &\quad&\text{in } \Omega, \\ u&=0 &\quad&\text{on } \partial\Omega, \endalignedat \tag{1.1} \end{equation} where $\Omega \subset {\mathbb R}^N$ is a bounded domain with smooth boundary $\partial \Omega$, a function $g\colon\Omega\times{\mathbb R}\to {\mathbb R}$ is of class $C^1$ such that $g(x,0)=0$ and which is asymptotically linear at infinity. We considered both cases, resonant and nonresonant. We use critical groups to distinguish the critical points.
Citation
Francisco O. V. de Paiva. "Multiple solutions for asymptotically linear resonant elliptic problems." Topol. Methods Nonlinear Anal. 21 (2) 227 - 247, 2003.
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