Existence of multiple solutions for a singular elliptic problem with critical Sobolev exponent (Q1938300)

Summary: We consider the existence of multiple solutions of the singular elliptic problem \(-\text{div}(| x|^{-ap}|\nabla u|^{p-2} \nabla u) + | u|^{p-2} u/| x|^{(a+1)p} = f| u|^{r-2} u + h| u|^{s-2} u + | x|^{-bp^\ast} | u|^{p^\ast -2} u, u(x) \rightarrow 0\) as \(| x| \rightarrow +\infty\), where \(x \in \mathbb R^N, 1 < p < N, a < (N - p)/p, a \leq b \leq a + 1, r, s > 1, p^\ast = Np/(N - pd), d = a + 1 - b\). By the variational method and the theory of genus, we prove that the above-mentioned problem has infinitely many solutions when some conditions are satisfied.