# Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation

Volume 9, Issue 4, pp 1432--1439
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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

•  46E20
•  35J10

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