Results 51 to 60 of about 33,794 (182)

Existence of solutions to quasilinear elliptic systems with combined critical Sobolev-Hardy terms

Electronic Journal of Differential Equations, 2012
This article is devoted to the study of multiple positive solutions to a singular elliptic system where the nonlinearity involves a combination of concave and convex terms.
Nemat Nyamoradi, Mohamad Javidi
doaj  

Existence and stability of solitons for the nonlinear Schr\"odinger equation on hyperbolic space

, 2014
We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space ...
Berestycki H, Hans Christianson, Jeremy L Marzuola, Lieb E H, Lions P-L, Lions P-L, Sulem C   +6 more
core   +1 more source

Uniform Continuity and Br\'ezis-Lieb Type Splitting for Superposition Operators in Sobolev Space [PDF]

, 2016
Using concentration-compactness arguments we prove a variant of the Brezis-Lieb-Lemma under weaker assumptions on the nonlinearity than known before.
Ackermann, Nils
core  

Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation

, 2011
We consider the nonlinear Schr\"{o}dinger equation $(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u$, $x\in \R^n$ with $V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_10\}}(x)+\Gamma_2(x) \chi_ ...
A. Pankov, A. Szameit, A. Szameit, C.A. Stuart, Ch.R. Rosberg, D. Arcoya, E. Blank, E. Korotyaev, G. Allaire, K. Makris, M. Renardy, M. Schechter, M. Struwe, Michael Plum, N.K. Efremidis, P.J.Y. Louis, P.L. Lions, R. Hempel, S. Mingaleev, S. Suntsov, T. Dohnal, T. Dohnal, Tomáš Dohnal, W.O. Amrein, Wolfgang Reichel, X. Wang, Y. Kartashov, Y.V. Kartashov   +27 more
core   +1 more source

Multiple solutions of a p-Kirchhoff equation with singular and critical nonlinearities

Electronic Journal of Differential Equations, 2017
In this article, we explore the existence of multiple solutions for a p-Kirchhoff equation with the nonlinearity containing both singular and critical terms.
Qin Li, Zuodong Yang, Zhaosheng Feng
doaj  

Existence of positive ground state solutions of Schrödinger–Poisson system involving negative nonlocal term and critical exponent on bounded domain

Boundary Value Problems, 2019
In this paper, we prove the existence of positive ground state solutions of the Schrödinger–Poisson system involving a negative nonlocal term and critical exponent on a bounded domain.
Wenxuan Zheng, Wenbin Gan, Shibo Liu
doaj   +1 more source

The concentration-compactness principle for fractional Orlicz-Sobolev spaces

Complex Variables and Elliptic Equations
In this paper, we delve into the well-known concentration-compactness principle in fractional Orlicz-Sobolev spaces, and we apply it to establish the existence of a weak solution for a critical elliptic problem involving the fractional $g-$Laplacian.
Bahrouni, Sabri, Miyagaki, Olimpio
openaire   +2 more sources

Doubly Critical Problems Involving Fractional Laplacians in ℝN

Advanced Nonlinear Studies, 2017
In this paper, we show the existence of nontrivial solutions for doubly critical nonlocal elliptic problems in ℝN{\mathbb{R}^{N}} involving fractional Laplacians.
Yang Jianfu, Wu Fengjie
doaj   +1 more source

Ground state solutions for asymptotically periodic Schrodinger equations with critical growth

Electronic Journal of Differential Equations, 2013
Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.
Hui Zhang, Junxiang Xu, Fubao Zhang
doaj  

Existence for (p, q) critical systems in the Heisenberg group

Advances in Nonlinear Analysis, 2019
This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (𝓢) in the Heisenberg group ℍn, driven by general (p, q) elliptic operators of Marcellini types.
Pucci Patrizia, Temperini Letizia
doaj   +1 more source