Existence and multiplicity of solutions for Kirchhoff–Schrödinger–Poisson system with critical growth

2021 ◽  
Author(s):  
Guofeng Che ◽  
Haibo Chen
Keyword(s):  
Variational Methods ◽  
Critical Growth ◽  
Poisson System ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

This paper is concerned with the following Kirchhoff–Schrödinger–Poisson system: [Formula: see text] where constants [Formula: see text], [Formula: see text] and [Formula: see text] are the parameters. Under some appropriate assumptions on [Formula: see text], [Formula: see text] and [Formula: see text], we prove the existence and multiplicity of nontrivial solutions for the above system via variational methods. Some recent results from the literature are greatly improved and extended.

scholarly journals Existence and multiplicity of solutions for a fractional p-Laplacian equation with perturbation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhen Zhi ◽  
Lijun Yan ◽  
Zuodong Yang
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Analytical Techniques ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

AbstractIn this paper, we consider the existence of nontrivial solutions for a fractional p-Laplacian equation in a bounded domain. Under different assumptions of nonlinearities, we give existence and multiplicity results respectively. Our approach is based on variational methods and some analytical techniques.

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

scholarly journals Concentration results for a magnetic Schrödinger-Poisson system with critical growth

2020 ◽  
Vol 10 (1) ◽  
pp. 775-798
Author(s):  
Jingjing Liu ◽  
Chao Ji
Keyword(s):  
Variational Methods ◽  
Nonlinear Term ◽  
Type Equation ◽  
Critical Growth ◽  
Poisson System ◽  
Nontrivial Solutions ◽  
Penalization Technique ◽  
Poisson Type

Abstract This paper is concerned with the following nonlinear magnetic Schrödinger-Poisson type equation $$\begin{array}{} \displaystyle \left\{ \begin{aligned} &\Big(\frac{\epsilon}{i}\nabla-A(x)\Big)^{2}u+V(x)u+\epsilon^{-2}(\vert x\vert^{-1}\ast \vert u\vert^{2})u=f(|u|^{2})u+\vert u\vert^{4}u \quad \hbox{in }\mathbb{R}^3,\\ &u\in H^{1}(\mathbb{R}^{3}, \mathbb{C}), \end{aligned} \right. \end{array}$$ where ϵ > 0, V : ℝ3 → ℝ and A : ℝ3 → ℝ3 are continuous potentials, f : ℝ → ℝ is a subcritical nonlinear term and is only continuous. Under a local assumption on the potential V, we use variational methods, penalization technique and Ljusternick-Schnirelmann theory to prove multiplicity and concentration of nontrivial solutions for ϵ > 0 small.

scholarly journals Multiple positive bound states for critical Schrödinger-Poisson systems

2019 ◽  
Vol 25 ◽  
pp. 73 ◽  
Author(s):  
Giovanna Cerami ◽  
Riccardo Molle
Keyword(s):  
Variational Methods ◽  
Ground State ◽  
Bound States ◽  
Nonlinear Term ◽  
Critical Growth ◽  
Poisson System ◽  
Lack Of Compactness ◽  
Ground State Solutions ◽  
Existence And Multiplicity

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrödinger-Poisson system: [see formula in PDF] We remark that (SP) exhibits a “double” lack of compactness because of the unboundedness of ℝ3 and the critical growth of the nonlinear term and that in our assumptions ground state solutions of (SP) do not exist.

Existence and multiplicity of solutions of Schrödinger—Poisson systems with radial potentials

2014 ◽  
Vol 144 (2) ◽  
pp. 319-332 ◽  
Author(s):  
Anran Li ◽  
Jiabao Su ◽  
Leiga Zhao
Keyword(s):  
Variational Methods ◽  
Infinitely Many Solutions ◽  
Poisson System ◽  
Radial Solutions ◽  
Radial Functions ◽  
Multiplicity Of Solutions ◽  
Nonlinear Schrödinger ◽  
Existence And Multiplicity ◽  
Image Position

In this paper, we deal with the nonlinear Schrödinger–Poisson systemwhere λ > 0, V and Q are radial functions, which can be vanishing or coercive at ∞. With assumptions on f just in a neighbourhood of the origin, existence and multiplicity of non-trivial radial solutions are obtained via variational methods. In particular, if f is sublinear and odd near the origin, we obtain infinitely many solutions of (SP)λ for any λ < 0.

EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR DEGENERATE HEMIVARIATIONAL INEQUALITIES INVOLVING LERAY–LIONS TYPE OPERATOR WITH CRITICAL GROWTH

2013 ◽  
Vol 11 (01) ◽  
pp. 1350007
Author(s):  
KAIMIN TENG
Keyword(s):  
Critical Growth ◽  
Type Operator ◽  
Hemivariational Inequalities ◽  
Concentration Compactness ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Concentration Compactness Principle ◽  
Nonsmooth Critical Point ◽  
Critical Point Theorems ◽  
Compactness Principle

In this paper, we investigate a hemivariational inequality involving Leray–Lions type operator with critical growth. Some existence and multiple results are obtained through using the concentration compactness principle of P. L. Lions and some nonsmooth critical point theorems.

scholarly journals SUPERLINEAR ELLIPTIC PROBLEMS WITH SIGN CHANGING COEFFICIENTS

2012 ◽  
Vol 14 (01) ◽  
pp. 1250001 ◽  
Author(s):  
EUGENIO MASSA ◽  
PEDRO UBILLA
Keyword(s):  
Variational Methods ◽  
Critical Case ◽  
Elliptic Problems ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Suitable Space

Via variational methods, we study multiplicity of solutions for the problem [Formula: see text] where a simple example for g(x, u) is |u|p-2u; here a, λ are real parameters, 1 < q < 2 < p ≤ 2* and b(x) is a function in a suitable space Lσ. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any λ > 0, and a total of five nontrivial solutions are obtained when λ is small and a ≥ λ1. Note that this type of results are valid even in the critical case.

scholarly journals Existence and Multiplicity of Positive Solutions for Schrödinger-Kirchhoff-Poisson System with Singularity

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mengjun Mu ◽  
Huiqin Lu
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Nehari Manifold ◽  
Poisson System ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
The Nehari Manifold

We study a singular Schrödinger-Kirchhoff-Poisson system by the variational methods and the Nehari manifold and we prove the existence, uniqueness, and multiplicity of positive solutions of the problem under different conditions.

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