Multiplicity of solutions for nonhomogeneous nonlinear elliptic equations with critical exponents. (Q696170)

This paper is devoted to the existence and multiplicity of solutions of problem \[ -\Delta u=u^{2^*-2}u+f \quad\text{in }\Omega, \qquad u>0 \quad\text{in }\Omega, \qquad u=0 \quad\text{on }\partial\Omega, \tag{1} \] where \(2^*:=\frac{2N}{N-2}\) is the critical Sobolev exponent, \(N\geq 3\), \(f\in C(\overline{\Omega})\) with \(f\not\equiv 0\) and \(f\geq 0\) on \(\Omega\). Here \(\Omega\) is a bounded domain in \(\mathbb R^N\) with smooth boundary. The author investigates the effect of the topology of \(\Omega\) on the multiple existence of solutions.