On superlinear Schrödinger equations with periodic potential

2011 ◽  
Vol 45 (1-2) ◽  
pp. 1-9 ◽  
Author(s):  
Shibo Liu
Keyword(s):  
Periodic Potential ◽  
Schrodinger Equations ◽  
Schrödinger Equations

scholarly journals Positive ground state solutions for asymptotically periodic generalized quasilinear Schrödinger equations

2021 ◽  
Vol 7 (1) ◽  
pp. 1015-1034
Author(s):  
Shulin Zhang ◽  
◽  
Keyword(s):  
Variational Method ◽  
Ground State ◽  
Periodic Potential ◽  
Ground State Solution ◽  
State Solution ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Asymptotically Periodic

<abstract><p>In this paper, we study the existence of a positive ground state solution for a class of generalized quasilinear Schrödinger equations with asymptotically periodic potential. By the variational method, a positive ground state solution is obtained. Compared with the existing results, our results improve and generalize some existing related results.</p></abstract>

Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations

1998 ◽  
Vol 128 (6) ◽  
pp. 1249-1260 ◽  
Author(s):  
Silvia Cingolani ◽  
Margherita Nolasco
Keyword(s):  
Periodic Boundary ◽  
Periodic Potential ◽  
Periodic Boundary Conditions ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Stationary States ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Semiclassical States

For a class of nonlinear Schrodinger equations, we prove the existence of semiclassical stationary states with possibly infinitely many concentration points. As h → 0, these states concentrate near critical points of the potential. Furthermore, for periodic potential, these states can be constructed to satisfy periodic boundary conditions.

Existence of solutions of non-linear Schrödinger equations

1977 ◽  
Vol 76 (3) ◽  
pp. 227-232 ◽  
Author(s):  
Klaus Schmitt ◽  
Long-yi Tsai
Keyword(s):  
Periodic Potential ◽  
Differential Operators ◽  
Existence Of Solutions ◽  
Type Theorem ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Non Linear ◽  
Existence Of Periodic Solutions ◽  
Linear Differential ◽  
Intermediate Value

SynopsisThe existence of periodic solutions of non-linear Schrödinger equations with periodic potential is investigated. The main result obtained is an intermediate value type theorem for such non-linear differential operators.

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