Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation | Zendy

Huxiao Luo | Zendy

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Ground state solutions for an asymptotically periodic and superlinear Schrodinger equation

Author(s) -

Huxiao Luo

Publication year - 2016

Publication title -

the journal of nonlinear sciences and applications

Language(s) - English

Resource type - Journals

eISSN - 2008-1901

pISSN - 2008-1898

DOI - 10.22436/jnsa.009.04.03

Subject(s) - mathematics , ground state , schrödinger's cat , schrödinger equation , state (computer science) , mathematical physics , mathematical analysis , quantum mechanics , physics , algorithm

We consider the semilinear Schrödinger equation { −4 u+ V (x)u = f(x, u), x ∈ RN , u ∈ H1(RN ), 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. c ©2016 All rights reserved.

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