scholarly journals Existence and multiplicity of solutions for fractional Schödinger equation involving a critical nonlinearity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongzhen Yun ◽  
Tianqing An ◽  
Guoju Ye
Keyword(s):  
Variational Method ◽  
Existence Results ◽  
Critical Growth ◽  
Concentration Compactness ◽  
Critical Nonlinearity ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

AbstractIn this paper, we investigate the fractional Schödinger equation involving a critical growth. By using the principle of concentration compactness and the variational method, we obtain some new existence results for the above equation, which improve the related results on this topic.

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 Existence and multiplicity of solutions for a Kirchhoff system with critical growth

2021 ◽  
Vol 46 (1) ◽  
pp. 295-308
Author(s):  
Marcelo F. Furtado ◽  
Luan D. de Oliveira ◽  
João Pablo P. da Silva
Keyword(s):  
Critical Growth ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

scholarly journals Existence and multiplicity of solutions for anisotropic elliptic equation

2022 ◽  
Vol 40 ◽  
pp. 1-12
Author(s):  
El Amrouss Abdelrachid ◽  
Ali El Mahraoui
Keyword(s):  
Elliptic Equation ◽  
Variational Method ◽  
Nonlinear Problem ◽  
Multiplicity Of Solutions ◽  
Anisotropic Elliptic Equation ◽  
Existence And Multiplicity

In this article we study the nonlinear problem $$\left\{ \begin{array}{lr} -\sum_{i=1}^{N}\partial_{x_{i}}a_{i}(x,\partial_{x_{i}}u)+ b(x)~|u|^{P_{+}^{+}-2}u =\lambda f(x,u) \quad in \quad \Omega\\ u=0 \qquad on \qquad \partial\Omega \end{array} \right.$$ Using the variational method, under appropriate assumptions on $f$, we obtain a result on existence and multiplicity of solutions.

scholarly journals Positive Solutions for Schrödinger-Poisson Systems with Sign-Changing Potential and Critical Growth

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Pengfei He ◽  
Hongmin Suo
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Critical Growth ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Multiplicity Of Positive Solutions

In this paper, we study the existence of positive solutions for Schrödinger-Poisson systems with sign-changing potential and critical growth. By using the analytic techniques and variational method, the existence and multiplicity of positive solutions are obtained.

Multiplicity of solutions for a nonlocal nonhomogeneous Neumann boundary problem with two critical exponents

2021 ◽  
pp. 1-22
Author(s):  
Augusto Costa ◽  
Andréia Pinheiro
Keyword(s):  
Variational Method ◽  
Boundary Value Problems ◽  
Boundary Problem ◽  
Critical Exponents ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Critical Growth ◽  
Multiplicity Of Solutions ◽  
Neumann Boundary Value Problems

This article concerns the multiplicity of solutions for a class of nonlocal and nonhomogeneous Neumann boundary value problems involving the p ( x )-Laplacian, in which both nonlinear terms assume critical growth. We use variational method, exploring an important truncation argument and properties of the genus.

Sign in / Sign up

Export Citation Format

Share Document