Multiplicity of solutions for nonhomogeneuous nonlinear elliptic equations with critical exponents
Keywords
Critical Sobolev, Dirichlet boundary value problem, semilinear elliptic problemAbstract
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.Downloads
Published
2001-12-01
How to Cite
1.
HIRANO, Norimichi. Multiplicity of solutions for nonhomogeneuous nonlinear elliptic equations with critical exponents. Topological Methods in Nonlinear Analysis. Online. 1 December 2001. Vol. 18, no. 2, pp. 269 - 281. [Accessed 29 March 2024].
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