Infinitely many solutions for quasilinear
schr\”{o}dinger equation with general superlinear
nonlinearity
Abstract
In this article, we study the quasilinear
Schr\”{o}dinger equation
\begin{eqnarray*} \begin{array}{ll}
\triangle{u}+V(x)u-\triangle(u^2)u=g(x,u),
\ x\in\mathbb{R}^N,
\end{array} \end{eqnarray*} where the
potential $V(x)$ and the primitive of $g(x,u)$ is allowed to be
sign-changing. Under more general superlinear conditions on $g$, we
obtain the existence of infinitely many nontrivial solutions by using
Mountain Pass Theorem. Recent results in the literature are
significantly improved.