Results 91 to 100 of about 4,702,923 (209)

Existence and multiplicity of positive solutions for Kirchhoff type equations at the critical frequency

Electronic Journal of Qualitative Theory of Differential Equations
We consider the following Kirchhoff equation with critical Sobolev exponent \begin{equation}\label{eq0} \begin{cases} \left(a+b\displaystyle\int_{\mathbb{R}^{N}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right)(-\Delta)^{s}u=|u|^{2^{*}_{s}-2}u+\mu g(x), \quad ...
Juhua He, Sijian You
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The Numbers of Positive Solutions by the Lusternik-Schnirelmann Category for a Quasilinear Elliptic System Critical with Hardy Terms

Abstract and Applied Analysis, 2019
In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains.
Mustapha Khiddi
doaj   +1 more source

Fourth order Hardy-Sobolev equations: Singularity and doubly critical exponent [PDF]

, 2023
In dimension $N\geq 5$, and for ...
Ali, Hussein Cheikh
core  

Multiplicity results for nonlinear elliptic equations involving critical Sobolev exponent

, 1986
SynopsisIn this paper we study the following boundary value problemwhere Ω is a bounded domain in Rn, n≧3, x ∈Rn, p* = 2n/(n – 2) is the critical exponent for the Sobolev embedding is a real parameter and f(x, t) increases, at infinity, more slowly than .
A. Capozzi, G. Palmieri
core   +1 more source

Existence of solutions for elliptic systems with critical Sobolev exponent

Electronic Journal of Differential Equations, 2002
We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.
Pablo Amster, Pablo De Napoli, Maria Cristina Mariani   +2 more
doaj  

A weighted Hardy-Sobolev-Maz’ya inequality [PDF]

, 2014
We provide a weighted extension of a Hardy-Sobolev-Maz’ya inequality that is due to Filippas, Maz’ya and ...
Sourdis, Christos
core  

On a potential-well type result and global bounds of solutions for semilinear parabolic equation involving critical Sobolev exponent (Analysis on Shapes of Solutions to Partial Differential Equations) [PDF]

, 2018
In this note, we are concerned with the asymptotics of (mainly nonnegative) solutions for a semilinear parabolic equation involving critical Sobolev exponent. The existence of a potential-well structure is discussed.
Ishiwata, Michinori
core  

On the location of the peaks of least-energy solutions to semilinear Dirichlet problems with critical growth

Abstract and Applied Analysis, 2002
We study the location of the peaks of solution for the critical growth problem −ε 2Δu+u=f(u)+u 2*−1, u>0 in Ω, u=0 on ∂Ω, where Ω is a bounded domain; 2*=2N/(N−2), N≥3, is the critical Sobolev exponent and f has a behavior like up ...
Marco A. S. Souto
doaj   +1 more source

The variable exponent BV-Sobolev capacity [PDF]

, 2020
In this article we study basic properties of the mixed BV-Sobolev capacity with variable exponent p. We give an alternative way to define mixed type BV-Sobolev-space which was originally introduced by Harjulehto, Hästö, and Latvala.
Matti Nuortio, Heikki Hakkarainen
core  

Existence of solutions for Choquard equations with an L 1 $L^{1}$ -integrable reciprocal potential and upper critical growth

Boundary Value Problems
This paper is dedicated to studying the Choquard-type equation { − Δ u + V ( x ) u = ( I α ∗ | u | p ) | u | p − 2 u + λ | u | q − 2 u , u ∈ H 1 ( R N ) , $$ \left \{ \textstyle\begin{array}{l} - \Delta u + V(x)u = ( {{I_{\alpha }} * {{\left | u \right |}
Ting Guo, Tianle Xia, Xianhua Tang
doaj   +1 more source