Nontrivial solutions of semilinear schrödinger equations on irnand strip-like domains

1995 ◽  
Vol 56 (3-4) ◽  
pp. 335-350 ◽  
Author(s):  
Stefan Tersian
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

scholarly journals Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Gauge Field ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Semilinear Elliptic ◽  
Chern Simons

We discuss the nonexistence of nontrivial solutions for the Chern-Simons-Higgs and Chern-Simons-Schrödinger equations. The Derrick-Pohozaev type identities are derived to prove it.

scholarly journals Existence of Nontrivial Solutions for Periodic Schrödinger Equations with New Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shaowei Chen ◽  
Dawei Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nontrivial Solution ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions

We study the Schrödinger equation:-Δu+Vxu+fx,u=0,  u∈H1(RN), whereVis1-periodic andfis1-periodic in thex-variables;0is in a gap of the spectrum of the operator-Δ+V. We prove that, under some new assumptions forf, this equation has a nontrivial solution. Our assumptions for the nonlinearityfare very weak and greatly different from the known assumptions in the literature.

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