Ground state solution and nodal solution for fractional nonlinear Schrödinger equation with indefinite potential

2019 ◽  
Vol 60 (4) ◽  
pp. 041501 ◽  
Author(s):  
Yuan Li ◽  
Dun Zhao ◽  
Qingxuan Wang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
Nonlinear Schrodinger Equation ◽  
State Solution ◽  
Nodal Solution ◽  
Indefinite Potential ◽  
Fractional Nonlinear Schrödinger Equation

Solutions on a torus for a semilinear equation

2011 ◽  
Vol 141 (2) ◽  
pp. 371-382
Author(s):  
Geneviéve Allain ◽  
Anne Beaulieu
Keyword(s):  
Schrödinger Equation ◽  
Small Parameter ◽  
Periodic Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
Nonlinear Schrodinger Equation ◽  
State Solution ◽  
Semilinear Equation

We are interested in the positive doubly periodic solutions, which are even in each variable, of a stationary nonlinear Schrödinger equation in ℝ2, with a small parameter. For any pair of periods (2a, 2b), we construct a branch of solutions that concentrate uniformly to the ground-state solution of the equation.

Existence of a Ground State Solution for a Quasilinear Schrödinger Equation

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Xiang-dong Fang ◽  
Zhi-qing Han
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Quasilinear Schrödinger Equation

AbstractIn this paper we are concerned with the quasilinear Schrödinger equation−Δu + V(x)u − Δ(uwhere N ≥ 3, 4 < p < 4N/(N − 2), and V(x) and q(x) go to some positive limits V

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