Multiplicity of positive solutions for semilnear elliptic problems with antipodal symmetry

Norimichi Hirano

DOI: http://dx.doi.org/10.12775/TMNA.2005.007

Abstract


In this paper, we show the multiple existence of positive solutions of
semilinear elliptic problems of the form
$$
-\Delta u=\vert u\vert ^{2^{*}-2}u+f, \quad u\in H_{0}^{1}(\Omega),
$$
where $\Omega\subset{\mathbb R}^{N}$ is a bounded domain, $2^{*}$ is the
Sobolev critical exponent and $f\in L^{2}(\Omega)$.

Keywords


Critical exponent; multiple existence; semilinear elliptic problem

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