Existence and multiplicity of solutions for generalized quasilinear Schrödinger equations

2021 ◽  
pp. 1-22
Author(s):  
Xue-Lin Gui ◽  
Bin Ge
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

scholarly journals Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Dong-Lun Wu
Keyword(s):  
Growth Conditions ◽  
Schrodinger Equations ◽  
Linking Theorem ◽  
Infinitely Many Solutions ◽  
Schrödinger Equations ◽  
Fountain Theorem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Working Space ◽  
Variant Fountain Theorem

In this study, we consider the following sublinear Schrödinger equations −Δu+Vxu=fx,u,for x∈ℝN,ux⟶0,asu⟶∞, where fx,u satisfies some sublinear growth conditions with respect to u and is not required to be integrable with respect to x. Moreover, V is assumed to be coercive to guarantee the compactness of the embedding from working space to LpℝN for all p∈1,2∗. We show that the abovementioned problem admits at least one solution by using the linking theorem, and there are infinitely many solutions when fx,u is odd in u by using the variant fountain theorem.

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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