Multiplicity of solutions for an elliptic problem with critical Sobolev-Hardy exponents and concave-convex nonlinearities (Q2443781)

Summary: We study the existence of multiple solutions for the following elliptic problem: \(-\Delta_p u - \mu(|u|^{p-2}u/|x|^p)=(|u|^{p^\ast (t)-2}/|x|^t)u+\lambda(|u|^{q-2}/|x|^s)u\), \(u \in W^{1,p}_o(\Omega)\). We prove that if \(1\leq q < p < N\), then there is a \(\mu_0\), such that for any \(\mu \in (0, \mu_0)\), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result of \textit{J. Garcia Azorero} and \textit{I. Peral Alonso} [Trans. Am. Math. Soc. 323, No. 2, 877--895 (1991; Zbl 0729.35051)].