Nehari-Type Ground State Solutions for Superlinear Elliptic Equations with Variable Exponent in ${\mathbb {R}}^N$

Abstract

We deal with the existence of Nehari-type ground state solutions for the superlinear p(x)-Laplacian equation

$$\begin{aligned} -\triangle _{p(x)} u+V(x)|u|^{p(x)-2}u= f(x,u),\; x\in {\mathbb {R}}^N,\;u\in W^{1,p(x)}({\mathbb {R}}^N). \end{aligned}$$

Under a weaker Nehari condition, we establish some existence criteria to guarantee that the above problem has Nehari-type ground state solutions using Non-Nehari manifold method.