The Existence Of Ground State Solutions For P-laplacian Equations With A General Critical Nonlinearity

In this paper,we study the following p-Laplacian equations with critical non-linearity-?pu+V(x)|u|p-2u=f(u),u?W1,p(RN),where p?(1,N),the potential V(x)?C1(RN,R)and the nonlinearity f(t)?|t|p*-2t+|t|q-2t(p<q<p*)does not satisfy the(AR)condition.Combining the monotonicity trick and global compactness lemma,we prove the existence of posi-tive ground state solutions for the given equation.Our result extends the main result in[J.Zhang,J.Math.Anal.Appl.,401(2013),232-241]con-cerning the existence of ground state solutions for p-Laplacian equation with constant potential.