Multiple sign-changing solutions for nonlinear Schrödinger equations with potential well

2019 ◽  
Vol 99 (15) ◽  
pp. 2555-2570
Author(s):  
Qingfei Jin
Keyword(s):  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Potential Well ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Sign Changing Solutions

scholarly journals SIGN-CHANGING SOLUTIONS FOR A CLASS OF NONLINEAR SCHRÖDINGER EQUATIONS

2009 ◽  
Vol 80 (2) ◽  
pp. 294-305 ◽  
Author(s):  
XIANGQING LIU ◽  
YISHENG HUANG
Keyword(s):  
Variational Methods ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Potential Well ◽  
Asymptotically Linear ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Sign Changing Solutions

AbstractUsing variational methods, we obtain the existence of sign-changing solutions for a class of asymptotically linear Schrödinger equations with deepening potential well.

NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL

2001 ◽  
Vol 03 (04) ◽  
pp. 549-569 ◽  
Author(s):  
THOMAS BARTSCH ◽  
ALEXANDER PANKOV ◽  
ZHI-QIANG WANG
Keyword(s):  
Essential Spectrum ◽  
Model Equation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Potential Well ◽  
Local Minima ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Steep Potential Well

We investigate nonlinear Schrödinger equations like the model equation [Formula: see text] where the potential Vλ has a potential well with bottom independent of the parameter λ > 0. If λ → ∞ the infimum of the essential spectrum of -Δ + Vλ in L2(ℝN) converges towards ∞ and more and more eigenvalues appear below the essential spectrum. We show that as λ→∞ more and more solutions of the nonlinear Schrödinger equation exist. The solutions lie in H1(ℝN) and are localized near the bottom of the potential well, but not near local minima of the potential. We also investigate the decay rate of the solutions as |x|→∞ as well as their behaviour as λ→∞.

Ground States for Nonlinear Schrödinger Equations with a Sign-changing Potential Well

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Zhi-Qiang Wang ◽  
Jiankang Xia
Keyword(s):  
Ground State ◽  
Ground States ◽  
Nehari Manifold ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Potential Well ◽  
Nonlinear Schrödinger ◽  
Variational Functional ◽  
Nonlinear Schrodinger Equations

AbstractIn this paper, we consider the ground state solutions for a class of nonlinear Schrödinger equationswhere 2 < p < 2*. We investigate the case λ > inf σ (−Δ + V), i.e., an indefinite problem.We characterize the ground states as minimizers of the variational functional on a modified Nehari manifold.

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