Solutions for a singular elliptic problem involving the p(x)-Laplacian

Abstract

Here, a singular elliptic problem involving p(x)−Laplacian operator in a bounded domain in R N is considered. Due to this, the existence of critical points for the energy functional which is unbounded below and satisfies the Palais-Smale condition are proved.

A weak solution for a $(p(x),q(x))$-Laplacian elliptic problem with a singular term

“…The differential operator p + q is known as the (p, q)-Laplacian operator, if p = q, where j , j > 1 denotes the j-Laplacian defined by j u := div(|∇u| j-2 ∇u). It is not homogeneous, thus some technical difficulties arise in applying the usual methods of the theory of elliptic equations (for further details, see [1,2,5,7,8,10,[12][13][14][15][16][19][20][21][22][23] and references therein).…”