Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation

Volume 9, Issue 4, pp 1432--1439 http://dx.doi.org/10.22436/jnsa.009.04.03

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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.

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Keywords

• Schrödinger equation
• ground state solutions
• asymptotically periodic
• sign-changing
• super-quadratic condition.

MSC

•  46E20
•  35J10

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