Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation
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Authors
Huxiao Luo
- School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P. R. China.
Abstract
We consider the semilinear Schrödinger 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.
Share and Cite
ISRP Style
Huxiao Luo, Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 4, 1432--1439
AMA Style
Luo Huxiao, Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation. J. Nonlinear Sci. Appl. (2016); 9(4):1432--1439
Chicago/Turabian Style
Luo, Huxiao. "Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation." Journal of Nonlinear Sciences and Applications, 9, no. 4 (2016): 1432--1439
Keywords
- Schrödinger equation
- ground state solutions
- asymptotically periodic
- sign-changing
- super-quadratic condition.
MSC
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