Dynamics of Partial Differential Equations
Volume 8 (2011)
On the quasilinear elliptic problem with a Hardy-Sobolev critical exponent
Pages: 225 – 237
In this article, we consider a quasilinear elliptic equation involving Hardy-Sobolev critical exponents and superlinear nonlinearity. The right hand side nonlinearity f(x, u) which is (p − 1)-superlinear nearby 0. However, it does not satisfy the usual Ambrosetti-Rabinowitz condition (AR-condition). Instead we employ a more general condition. Using a variational approach based on the critical point theory and the Ekeland variational principle, we show the existence of two nontrivial positive solutions. Moreover, the obtained results extend some existing ones.
p-Laplacian; Hardy-Sobolev critical exponent; (PS)c-condition; Mountain pass lemma; Ekeland variational principle
2010 Mathematics Subject Classification