Multiple solutions for asymptotically linear resonant elliptic problems
Słowa kluczowe
Cerami condition, multiplicity of solutions, double resonance, sign changing solutionAbstrakt
In this paper we establish the existence of multiple solutions for the semilinear elliptic problem $$\alignedat 2 -\Delta u&=g(x,u) &\quad&\text{in } \Omega, \\ u&=0 &\quad&\text{on } \partial\Omega, \endalignedat \tag 1.1 $$ 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.Pobrania
Opublikowane
2003-06-01
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1.
DE PAIVA, Francisco Odair. Multiple solutions for asymptotically linear resonant elliptic problems. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2003, T. 21, nr 2, s. 227–247. [udostępniono 3.7.2024].
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