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

Luo, Huxiao ¹

¹ School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P. R. China

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 4, p. 1432-1439

Résumé

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.

Détail

DOI : 10.22436/jnsa.009.04.03

Classification : 46E20, 35J10
Keywords: Schrödinger equation, ground state solutions, asymptotically periodic, sign-changing, super-quadratic condition.

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