Results 71 to 80 of about 33,794 (182)

A study and an application of the concentration compactness type principle

, 2019
In this article we develop a concentration compactness type principle in a variable exponent setup. As an application of this principle we discuss a problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power nonlinearities with exponents $(p^+)^*$, $p_s^*(x)$ with the assumption that the critical set $\{x\in :p_s^*(x)=(p^+)^*\}$ is nonempty.
Panda, Akasmika, Choudhuri, Debajyoti
openaire   +2 more sources

The Liouville Equation with Singular Data: A Concentration-Compactness Principle via a Local Representation Formula

Journal of Differential Equations, 2002
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BARTOLUCCI, DANIELE, TARANTELLO, GABRIELLA   +1 more
openaire   +2 more sources

A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN

Advanced Nonlinear Studies, 2017
This paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent:
Xiang Mingqi, Zhang Binlin, Zhang Xia
doaj   +1 more source

Stable solitary waves for one-dimensional Schrodinger-Poisson systems

Electronic Journal of Differential Equations, 2016
Based on the concentration compactness principle, we shoe the existence of ground state solitary wave solutions for one-dimensional Schrodinger-Poisson systems with large L2-norm in the energy space.
Guoqing Zhang, Weiguo Zhang, Sanyang Liu
doaj  

Multiple Solutions of a Nonlocal Problem with Nonlinear Boundary Conditions

Discrete Dynamics in Nature and Society
In this article, we consider a class of nonlocal p(x)-Laplace equations with nonlinear boundary conditions. When the nonlinear boundary involves critical exponents, using the concentration compactness principle, mountain pass lemma, and fountain theorem,
Jie Liu, Qing Miao
doaj   +1 more source

The concentration-compactness principle for Musielak-Orlicz spaces and applications

This paper extends the Concentration-Compactness Principle to Musielak-Orlicz spaces, working in both bounded and unbounded domains. We show that our results include important special cases like classical Orlicz spaces, variable exponent spaces, double phase spaces, and a new type of double phase problem where the exponents depend on the solution ...
Bahrouni, Ala Eddine, Bahrouni, Anouar
openaire   +2 more sources

On the lack of compactness on stratified Lie groups

, 2014
In $\mathbb{R}^d$, the characterization of the \mbox{lack of compactness of the continuous Sobolev injection $ \mathring{H}^s \hookrightarrow L^p $}, with $ \displaystyle{\frac{s}{d} + \frac{1}{p} = \frac{1}{2}} $ and $\displaystyle{
Wong, Chieh-Lei
core   +1 more source

Existence of solutions for logarithmic Kirchhoff equation without compactness in $\mathbb{R}^3$

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we investigate the logarithmic Kirchhoff-type equation \begin{align*} -\left(a+b\int_{\mathbb R^3}|\nabla u|^2 \mathrm{d}x\right)\Delta u+V(x)u=|u|^{p-2}u\log |u|, \quad x\in\mathbb {R}^3, \end{align*} where $a,b>0$ are constants,
Min Li, Libo Wang, Lihong Bao
doaj   +1 more source

Combined effects of changing-sign potential and critical nonlinearities in Kirchhoff type problems

Electronic Journal of Differential Equations, 2016
In this article, we study the existence and multiplicity of positive solutions for a class of Kirchhoff type problems involving changing-sign potential and critical growth terms.
Gao-Sheng Liu, Liu-Tao Guo, Chun-Yu Lei
doaj  

Fractional minimization problem on the Nehari manifold

Electronic Journal of Differential Equations, 2018
In the framework of fractional Sobolev space, using Nehari manifold and concentration compactness principle, we study a minimization problem in the whole space involving the fractional Laplacian.
Mei Yu, Meina Zhang, Xia Zhang
doaj