Existence of infinitely many solutions for elliptic problems with critical exponent (Q705397)

The authors deal with the following nonlinear problem: \[ -\Delta_pu=|u|^{p_*-2}u+\lambda f(x,u),\;x\in\Omega,\quad u=0\;\text{ on }\partial\Omega,\tag{1} \] where \(\Delta_pu=\text{div}(|\nabla u|^{p-2}\nabla u)\) is the \(p\)-Laplacian operator of \(u\), \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) \((N\geq 3)\), \(1<p<n\), \(p_*=\frac{p_n}{n-p}\) is the critical exponent for the Sobolev embedding, \(\lambda>0\) and \(f\) is a given \(f:\mathbb{R}^N\times\mathbb{R}\to\mathbb{R}\) function. The main goal of the authors is to establish the existence theorem of infinitely many solutions of (1).