Results 61 to 70 of about 4,030 (152)

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
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The concentration-compactness principles for $W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)$ and application

, 2019
We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.
Ho, Ky, Kim, Yun-Ho
openaire   +3 more sources

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
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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
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Existence and concentration of solutions for a p-laplace equation with potentials in R^N

Electronic Journal of Differential Equations, 2010
We study the p-Laplace equation with Potentials $$ -hbox{div}(| abla u|^{p-2} abla u)+lambda V(x)|u|^{p-2}u=|u|^{q-2}u, $$ $uin W^{1,p}(mathbb{R}^N)$, $xin mathbb{R}^N$ where $2leq p$, $p<q<p^{*}$. Using a concentration-compactness principle
Mingzhu Wu, Zuodong Yang
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Existence of positive solutions for Brezis-Nirenberg type problems involving an inverse operator

Electronic Journal of Differential Equations, 2021
Pablo Alvarez-Caudevilla, Eduardo Colorado, Alejandro Ortega   +2 more
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Existence of normalized solutions to Kirchhoff-Boussinesq equations in the subcritical and supercritical regime

Electronic Journal of Differential Equations
In this article we study the existence of normalized solutions to the Kirchhoff-Boussinesq equation under the mass constraint $\|u\|_{2}=c$. In the $L^{2}$-subcritical regime, we apply Ekeland's variational principle and concentration compactness method ...
Chunling Tao, Lintao Liu, Kaimin Teng
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Solitary waves for a coupled nonlinear Schrodinger system with dispersion management

Electronic Journal of Differential Equations, 2010
We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication.
Panayotis Panayotaros, Mauricio Sepulveda, Octavio Vera   +2 more
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Positive solutions to quasilinear equations involving critical exponent on perturbed annular domains

Electronic Journal of Differential Equations, 2005
In this paper we study the existence of positive solutions for the problem $$ -Delta_{p}u=u^{p^{*}-1} quad hbox{in } Omega quad hbox{and} quad u=0 quad hbox{on } partial{Omega} $$ where $Omega$ is a perturbed annular domain (see definition in the ...
Claudianor O. Alves
doaj  

Ground states for the fractional Schrodinger equation

Electronic Journal of Differential Equations, 2013
In this article, we show the existence of ground state solutions for the nonlinear Schrodinger equation with fractional Laplacian $$ (-Delta )^alpha u+ V(x)u =lambda |u|^{p}uquadhbox{in $mathbb{R}^N$ for $alpha in (0,1)$}.
Binhua Feng
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