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Ground State Solutions for Singular Quasilinear Elliptic Equations

Commun. Math. Anal.
Volume 9, Number 2 (2010), 12 - 21

Ground State Solutions for Singular Quasilinear Elliptic Equations

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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.]