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.

scholarly journals Existence of Solutions for a Schrödinger–Poisson System with Critical Nonlocal Term and General Nonlinearity

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Jiafeng Zhang ◽  
Wei Guo ◽  
Changmu Chu ◽  
Hongmin Suo
Keyword(s):  
Variational Method ◽  
Existence Of Solutions ◽  
Nonlocal Term ◽  
Poisson System ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Analysis Technique ◽  
General Nonlinearity

We study the existence and multiplicity of nontrivial solutions for a Schrödinger–Poisson system involving critical nonlocal term and general nonlinearity. Based on the variational method and analysis technique, we obtain the existence of two nontrivial solutions for this system.

scholarly journals Nonexistence Results for the Schrödinger-Poisson Equations with Spherical and Cylindrical Potentials in

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yongsheng Jiang ◽  
Yanli Zhou ◽  
B. Wiwatanapataphee ◽  
Xiangyu Ge
Keyword(s):  
Poisson System ◽  
Nontrivial Solutions ◽  
Radial Functions ◽  
Poisson Equations

We study the following Schrödinger-Poisson system: , , , where are positive radial functions, , , and is allowed to take two different forms including and with . Two theorems for nonexistence of nontrivial solutions are established, giving two regions on the plane where the system has no nontrivial solutions.

scholarly journals Multiple solutions for a quasilinear Schrödinger–Poisson system

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Zhang
Keyword(s):  
Nontrivial Solution ◽  
Ground State ◽  
Multiple Solutions ◽  
Continuous Functions ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
State Solution ◽  
Poisson System ◽  
Subcritical Growth ◽  
Monotonicity Properties

AbstractIn this article, we consider the following quasilinear Schrödinger–Poisson system $$ \textstyle\begin{cases} -\Delta u+V(x)u-u\Delta (u^{2})+K(x)\phi (x)u=g(x,u), \quad x\in \mathbb{R}^{3}, \\ -\Delta \phi =K(x)u^{2}, \quad x\in \mathbb{R}^{3}, \end{cases} $$ { − Δ u + V ( x ) u − u Δ ( u 2 ) + K ( x ) ϕ ( x ) u = g ( x , u ) , x ∈ R 3 , − Δ ϕ = K ( x ) u 2 , x ∈ R 3 , where $V,K:\mathbb{R}^{3}\rightarrow \mathbb{R}$ V , K : R 3 → R and $g:\mathbb{R}^{3}\times \mathbb{R}\rightarrow \mathbb{R}$ g : R 3 × R → R are continuous functions; g is of subcritical growth and has some monotonicity properties. The purpose of this paper is to find the ground state solution of (0.1), i.e., a nontrivial solution with the least possible energy by taking advantage of the generalized Nehari manifold approach, which was proposed by Szulkin and Weth. Furthermore, infinitely many geometrically distinct solutions are gained while g is odd in u.

scholarly journals The Existence of Nontrivial Solutions to a Class of Quasilinear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiaoyao Jia ◽  
Zhenluo Lou
Keyword(s):  
Sobolev Space ◽  
Variational Methods ◽  
Nontrivial Solution ◽  
Quasilinear Equation ◽  
Minimax Theorem ◽  
Nontrivial Solutions ◽  
Quasilinear Equations

In this paper, we study the following quasilinear equation: − div ϕ ∇ u ∇ u + ϕ u u = f u   in   ℝ N , where ϕ ∈ C 1 ℝ + , ℝ + and Φ t = ∫ 0 t s ϕ ∣ s ∣ d s . In the Orlicz-Sobolev space, by variational methods and a minimax theorem, we prove the equation has a nontrivial solution.

scholarly journals Nontrivial Solutions for Dirichlet Boundary Value Systems with the(p1,…,pn)-Laplacian

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shang-Kun Wang ◽  
Wen-Wu Pan
Keyword(s):  
Critical Point ◽  
Nontrivial Solution ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Nontrivial Solutions

Using critical point theory due to Bonanno (2012), we prove the existence of at least one nontrivial solution for Dirichlet boundary value systems with the(p1,…,pn)-Laplacian.

Sign in / Sign up

Export Citation Format

Share Document