Ground state solutions for an asymptotically periodic and superlinear Schrödinger equation
نویسندگان
چکیده
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.
منابع مشابه
Existence of Positive Ground State Solutions for a Class of Asymptotically Periodic Schrödinger-poisson Systems
In this article, by using variational method, we study the existence of a positive ground state solution for the Schrödinger-Poisson system −∆u+ V (x)u+K(x)φu = f(x, u), x ∈ R, −∆φ = K(x)u, x ∈ R, where V (x),K(x) and f(x, u) are asymptotically periodic functions in x at infinity.
متن کاملTwo Types of Ground State Solutions for a Periodic Schrödinger Equations with Zero on the Boundary of the Spectrum
This article concerns the Schrödinger equation −∆u+ V (x)u = f(x, u), for x ∈ R , u(x)→ 0, as |x| → ∞ . Assuming that V and f are periodic in x, and 0 is a boundary point of the spectrum σ(−∆ + V ), two types of ground state solutions are obtained with some super-quadratic conditions.
متن کاملAsymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases
We consider a class of nonlinear Schrödinger equations in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L) nonlinearities. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions ...
متن کاملMulti-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions
In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + V (x)u = f(x, u), u ∈ H1(RN). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x, t) satisfies some superlinear growth conditions and need not be odd or increasing strictly in t. Using a new variational reduction method and a generaliz...
متن کاملAsymptotic stability of ground states in 3D nonlinear Schrödinger equation including subcritical cases
We consider a class of nonlinear Schrödinger equation in three space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L) nonlinearities. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015