%0 Journal Article
%T Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation
%A Luo, Huxiao
%J Journal of Nonlinear Sciences and Applications
%D 2016
%V 9
%N 4
%@ ISSN 2008-1901
%F Luo2016
%X We consider the semilinear SchrÃ¶dinger equation
\[
\begin{cases}
-\Delta u + V(x)u= f(x,u) ,\,\,\,\,\, x\in R^N,\\
u\in H^1(R^N),
\end{cases}
\]
where V (x) is asymptotically periodic and sign-changing, f(x; u) is a superlinear, subcritical nonlinearity.
Under asymptotically periodic V (x) and a super-quadratic condition about f(x; u). We prove that the
above problem has a ground state solution which minimizes the corresponding energy among all nontrivial
solutions.
%9 journal article
%R 10.22436/jnsa.009.04.03
%U http://dx.doi.org/10.22436/jnsa.009.04.03
%P 1432--1439