scholarly journals Multiplicity of Solutions for Generalized Quasilinear Schrödinger Equations

2020 ◽  
Vol 63 (1) ◽  
pp. 11-40
Author(s):  
Guofa Li ◽  
◽  
Bitao Cheng ◽  
Keyword(s):  
Small Parameter ◽  
Existence Results ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Superlinear Growth

In this paper, we study the following quasilinear Schrödinger equations: (P) where are given potentials, is a small parameter, g is a even function with and for all and satisfies superlinear growth at infinity. We get the existence results of multiplicity of nontrivial solutions for problem

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 Multiplicity of Solutions for Schrödinger Equations with Concave-Convex Nonlinearities

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Dong-Lun Wu ◽  
Chun-Lei Tang ◽  
Xing-Ping Wu
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Multiplicity Of Solutions ◽  
Coercive Condition

We study the multiplicity of solutions for a class of semilinear Schrödinger equations: -Δu+V(x)u=gx,u,  for  x∈RN;  u(x)→0,  as  u→∞, where V satisfies some kind of coercive condition and g involves concave-convex nonlinearities with indefinite signs. Our theorems contain some new nonlinearities.

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