Results 31 to 40 of about 52,371 (280)

On a p-Laplacian system with critical Hardy–Sobolev exponents and critical Sobolev exponents [PDF]

open access: yesUkrainian Mathematical Journal, 2012
We consider a quasilinear elliptic system involving the critical Hardy–Sobolev exponent and the Sobolev exponent. We use variational methods and analytic techniques to establish the existence of positive solutions of the system.
openaire   +3 more sources

On a Minimization Problem Involving the Critical Sobolev Exponent

open access: yesAdvanced Nonlinear Studies, 2007
Abstract Following [3] we study the following minimization problem: in any dimension n ≥ 4 and under suitable assumptions on a(x).
PRINARI F, VISCIGLIA, NICOLA
openaire   +4 more sources

The Kato Square Root Problem for Mixed Boundary Conditions [PDF]

open access: yes, 2013
We consider the negative Laplacian subject to mixed boundary conditions on a bounded domain. We prove under very general geometric assumptions that slightly above the critical exponent $\frac{1}{2}$ its fractional power domains still coincide with ...
Egert, Moritz   +2 more
core   +1 more source

An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces

open access: yesAdvances in Nonlinear Analysis, 2020
It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
doaj   +1 more source

A fractional Kirchhoff problem involving a singular term and a critical nonlinearity [PDF]

open access: yes, 2017
In this paper we consider the following critical nonlocal problem $$ \left\{\begin{array}{ll} M\left(\displaystyle\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdy\right)(-\Delta)^s u = \displaystyle\frac{\lambda}{u^\gamma}+u^{2^*_s-1}&\quad ...
Fiscella, Alessio
core   +1 more source

Existence and concentration behavior of solutions for a class of quasilinear elliptic equations with critical growth

open access: yesAdvances in Nonlinear Analysis, 2017
In this paper, we study a class of quasilinear elliptic equations involving the Sobolev critical ...
Teng Kaimin, Yang Xiaofeng
doaj   +1 more source

Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

open access: yesBoundary Value Problems, 2021
In this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.
Hongsen Fan, Zhiying Deng
doaj   +1 more source

Normalized solutions for nonlinear Kirchhoff type equations in high dimensions

open access: yesElectronic Research Archive, 2022
We study the normalized solutions for nonlinear Kirchhoff equation with Sobolev critical exponent in high dimensions $ \mathbb{R}^N(N\geqslant4) $. In particular, in dimension $ N = 4 $, there is a special phenomenon for Kirchhoff equation that the mass ...
Lingzheng Kong, Haibo Chen
doaj   +1 more source

Positive solutions for a class of singular quasilinear Schrödinger equations with critical Sobolev exponent [PDF]

open access: yesJournal of Differential Equations, 2017
We prove the existence of positive solutions of the following singular quasilinear Schrodinger equations at critical growth − Δ u − λ c ( x ) u − κ α ( Δ ( | u | 2 α ) ) | u | 2 α − 2 u = | u | q − 2 u + | u | 2 ⁎ − 2 u , u ∈ D 1 , 2 ( R N ) , via ...
Zhouxin Li
semanticscholar   +1 more source

Existence of solution to a critical equation with variable exponent [PDF]

open access: yes, 2012
In this paper we study the existence problem for the $p(x)-$Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not ...
Bonder, Julián Fernández   +2 more
core   +1 more source

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