Variant fountain theorems and their applications

2001 ◽  
Vol 104 (3) ◽  
pp. 343-358 ◽  
Author(s):  
Wenming Zou
Keyword(s):  
Fountain Theorems ◽  
Variant Fountain Theorems

scholarly journals An Application of Variant Fountain Theorems to a Class of Impulsive Differential Equations with Dirichlet Boundary Value Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liu Yang
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Classical Solutions ◽  
Boundary Value Condition ◽  
Fountain Theorems ◽  
Variant Fountain Theorems

We consider the existence of infinitely many classical solutions to a class of impulsive differential equations with Dirichlet boundary value condition. Our main tools are based on variant fountain theorems and variational method. We study the case in which the nonlinearity is sublinear. Some recent results are extended and improved.

scholarly journals Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Wang ◽  
Yansheng Liu ◽  
Yujun Cui
Keyword(s):  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Point Theory ◽  
Fractional Boundary Value Problem ◽  
Fountain Theorems ◽  
Left And Right ◽  
Variant Fountain Theorems ◽  
Derivatives Of

This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux,  x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess  infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f:0,T×R→R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.

scholarly journals Existence and Multiplicity of Nontrivial Solutions for a Class of Semilinear Fractional Schrödinger Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Xinsheng Du ◽  
Anmin Mao
Keyword(s):  
Existence Of Solutions ◽  
High Energy ◽  
Sufficient Condition ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Fractional Schrödinger Equations ◽  
Fountain Theorems ◽  
Superquadratic Growth ◽  
Variant Fountain Theorems

This paper is concerned with the existence of solutions to the following fractional Schrödinger type equations: -∆su+Vxu=fx,u,  x∈RN, where the primitive of the nonlinearity f is of superquadratic growth near infinity in u and the potential V is allowed to be sign-changing. By using variant Fountain theorems, a sufficient condition is obtained for the existence of infinitely many nontrivial high energy solutions.

Existence of High Energy Solutions for Kirchhoff-Type Equations

2013 ◽  
Vol 765-767 ◽  
pp. 739-743 ◽  
Author(s):  
Chun Han Liu ◽  
Jian Guo Wang
Keyword(s):  
Growth Conditions ◽  
High Energy ◽  
Kirchhoff Type ◽  
Nonlocal Equations ◽  
Fountain Theorems

In this paper, by applying the fountain theorems, we study the existence of infinitely many high energy solutions for the nonlinear kirchhoff nonlocal equations under the Ambrosetti-Rabinowitz type growth conditions or no Ambrosetti-Rabinowitz type growth conditions, infinitely many high energy solutions are obtained.

scholarly journals Existence of Multiple Nontrivial Solutions for a Strongly Indefinite Schrödinger-Poisson System

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shaowei Chen ◽  
Liqin Xiao
Keyword(s):  
Nontrivial Solution ◽  
Infinitely Many Solutions ◽  
Poisson System ◽  
Nontrivial Solutions ◽  
Local Linking ◽  
Variational Functional ◽  
Indefinite Potential ◽  
Fountain Theorems ◽  
General Nonlinearity ◽  
Odd Nonlinearity

We consider a Schrödinger-Poisson system inℝ3with a strongly indefinite potential and a general nonlinearity. Its variational functional does not satisfy the global linking geometry. We obtain a nontrivial solution and, in case of odd nonlinearity, infinitely many solutions using the local linking and improved fountain theorems, respectively.

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