Ground State Solutions for Singular Quasilinear Elliptic Equations

Abstract

The existence of ground state solutions for the quasi-linear elliptic equation

$$-\mbox{div}(|\nabla u|^{p-2}\nabla u)=\rho(x)f(u),\;\;\mbox {in}\;\;{\bf R^N}$$

under suitable conditions is proved. We modify the method developed in [Z. Yang, Existence of positive entire solutions for singular and non-singular quasi-linear elliptic equation, J. Comput. Appl. Math. 197 (2006) 355-364] and extend the results of [A.Mohammed, Ground state solutions for singular semi-linear elliptic equations, Nonlinear Analysis(in press) and Teodora-Liliana Dinu, Entire solutions of sublinear elliptic equations in anisotropic media, J. Math. Anal. Appl. 322(2006), 382-392.]