### Multiplicity of positive solutions for semilnear elliptic problems with antipodal symmetry

#### 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 $f\in L^{2}(\Omega)$.

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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