Multiplicity of solutions for nonhomogeneuous nonlinear elliptic equations with critical exponents
Słowa kluczowe
Critical Sobolev, Dirichlet boundary value problem, semilinear elliptic problemAbstrakt
Let $N \geq 3$ and $\Omega \subset \mathbb R^{N} $ be a bounded domain with a smooth boundary $\partial \Omega $. We %In this paper we consider a semilinear boundary value problem of the form %existence and multiplicity of solutions of problem $$ \cases -\Delta u = \vert u\vert ^{2^*-2} u +f &\text{\rm in } \Omega,\\ u> 0 & \text{\rm in } \Omega, \\ u= 0 & \text{\rm on } \partial \Omega, \endcases \leqno \text{\rm (P)} $$ where $f \in C(\overline \Omega )$ and $2^* = 2N/(N-2)$. We show the effect of topology of $\Omega $ on the multiple existence of solutions.Pobrania
Opublikowane
2001-12-01
Jak cytować
1.
HIRANO, Norimichi. Multiplicity of solutions for nonhomogeneuous nonlinear elliptic equations with critical exponents. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 2001, T. 18, nr 2, s. 269–281. [udostępniono 3.7.2024].
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