GROUND STATE SOLUTIONS FOR -SUPERLINEAR -LAPLACIAN EQUATIONS
GROUND STATE SOLUTIONS FOR -SUPERLINEAR -LAPLACIAN EQUATIONS
Abstract In this paper, we deduce new conditions for the existence of ground state solutions for the $p$ -Laplacian equation $$\begin{equation*} \left \{ \begin{array}{@{}ll} -\mathrm {div}(|\nabla u|^{p-2}\nabla u)+V(x)|u|^{p-2}u=f(x, u), \quad x\in {\mathbb {R}}^{N},\\[5pt] u\in W^{1, p}({\mathbb {R}}^{N}), \end{array} \right . \end{equation*}$$ which weaken the Ambrosetti–Rabinowitz type condition and the monotonicity …