Results 111 to 120 of about 4,486,095 (208)

Nonhomogeneous elliptic problems of Kirchhoff type involving critical Sobolev exponents

Electronic Journal of Differential Equations, 2015
This article concerns the existence and the multiplicity of solutions for nonhomogeneous elliptic Kirchhoff problems involving the critical Sobolev exponent, defined on a regular bounded domain of $\mathbb{R}^3$.
Safia Benmansour, Mohammed Bouchekif
doaj  

An existence result for elliptic problems with singular critical growth

Electronic Journal of Differential Equations, 2007
We prove the existence of nontrivial solutions for the singular critical problem $$ -Delta u-mu frac{u}{|x|^{2}}=lambda f(x)u+u^{2^{ast }-1} $$ with Dirichlet boundary conditions.
Yasmina Nasri
doaj  

Multiple positive solutions for a critical elliptic problem with concave and convex nonlinearities

Electronic Journal of Differential Equations, 2014
In this article, we study the multiplicity of positive solutions for a semi-linear elliptic problem involving critical Sobolev exponent and concave-convex nonlinearities. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we prove
Haining Fan
doaj  

Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics. [PDF]

Arch Ration Mech Anal, 2021
Deng Y, Zillinger C.
europepmc   +1 more source

Multiple positive solutions for equations involving critical Sobolev exponent in R^N

Electronic Journal of Differential Equations, 1997
$$ -{ m div }(|abla u|^{m-2}abla u) = lambda h u^q+u^{m^*-1},quad{ m in}quad R^N,. $$ Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of $lambda ^*>0$ such that there are at least two non-negative solutions ...
Claudianor Oliveira Alves
doaj  

Spatial-temporal correlations in the speckle pattern for the characterization of cellular motion within a 3D object. [PDF]

Biomed Opt Express, 2023
Weil Y, Shafran Y, Sobolev M, Afrimzon E, Zurgil N, Deutsch M, Schiffer Z.   +6 more
europepmc   +1 more source

Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent

Electronic Journal of Differential Equations, 2006
In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent $$displaylines{ -Delta u = lambda u - alpha u^p+ u^{2^*-1}, quad u >0 , quad hbox{in } Omega,cr u=0, quad hbox ...
Yuanji Cheng
doaj  

Uniqueness of Solutions to Nonlinear Schrödinger Equations from their Zeros. [PDF]

Ann PDE, 2022
Kehle C, Ramos JPG.
europepmc   +1 more source

Multiplicity results for nonlinear elliptic equations

Electronic Journal of Differential Equations, 2006
Let $Omega$ be a bounded domain in $mathbb{R}^{N}$, $Ngeq 3$, and $p=frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $fin H^1_0(Omega)^ast$, satisfying suitable conditions, the nonlinear elliptic problem $$displaylines{ -Delta u =|u |^{ p ...
Samira Benmouloud, Mostafa Khiddi, Simohammed Sbai   +2 more
doaj  

Existence of solutions to fractional equations with Hardy potential on compact Riemannian manifolds

Electronic Journal of Differential Equations
In this article, we study a fractional Laplace equation on a compact Riemannian manifold involving a Hardy potential and a nonlinearity with critical exponent, $$ (-\Delta_g)^s u - \mu \frac{u}{d_g(x, x_0)^{2s}} = \lambda f(x)|u|^{p-2}u + k(x) |u|^{2_s^
Shengbing Deng, Fanyun Li
doaj