Results 81 to 90 of about 13,900 (197)

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

Communications on Pure and Applied Analysis, 2023
In dimension $N\geq 5$, and for ...
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Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight

Electronic Journal of Differential Equations, 2016
In this article we consider the problem $$\displaylines{ -\hbox{div}\big(p(x)\nabla u\big)=|u|^{2^{*}-2}u+\lambda f\quad \text{in }\Omega \cr u=0 \quad \text{on }\partial\Omega }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$, We study ...
Mohammed Bouchekif, Ali Rimouche
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A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent

, 2019
Let $(M,\textit{g},\sigma)$ be a compact Riemannian spin manifold of dimension $m\geq2$, let $\mathbb{S}(M)$ denote the spinor bundle on $M$, and let $D$ be the Atiyah-Singer Dirac operator acting on spinors $\psi:M\to\mathbb{S}(M)$.
Bartsch, Thomas, Xu, Tian
core  

Strongly indefinite systems with critical sobolev exponents and weights

Applied Mathematics Letters, 2004
Let \(\Omega\) be a bounded smooth domain in \(\mathbb R^N\), \(N\geq 4\) and \(\lambda,\mu\in\mathbb R\). The author deals with the following problem: \[ -\Delta v=\lambda u+K(x)|u|^{p-1}u\text{ in }\Omega, \quad -\Delta u=\mu v+ Q(x)|v|^{q-1}v\text{ in }\Omega, \quad u=v=0\text{ on }\partial\Omega, \tag{1} \] where \(p,q>1\) and coefficients \(K,Q ...
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Existence of nontrivial solutions for biharmonic equations with critical growth

Electronic Journal of Differential Equations
We consider the biharmonic equation with critical Sobolev exponent, $$ \Delta^2u-\Delta u-\Delta(u^2)u+V(x)u=|u|^{2^{**}-2}u+\alpha |u|^{p-2}u,\quad \text{in }\mathbb{R}^N, $$ where $N> 4$, $\alpha>0$, $V(x)$ is a given potential, $2^{**}=\frac{2N}{N-4}$
Juhua He, Ke Wu, Fen Zhou
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Two positive solutions for quasilinear elliptic equations with singularity and critical exponents

Boundary Value Problems, 2018
In this paper, we consider the quasilinear elliptic equation with singularity and critical exponents {−Δpu−μ|u|p−2u|x|p=Q(x)|u|p∗(t)−2u|x|t+λu−s,in Ω,u>0,in Ω,u=0,on ∂Ω, $$ \textstyle\begin{cases} -\Delta_{p}u-\mu \frac{ \vert u \vert ^{p-2}u}{ \vert x ...
Yanbin Sang, Xiaorong Luo, Zongyuan Zhu
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Quasilinear elliptic problems involving multiple critical Hardy–Sobolev exponents

Computers & Mathematics with Applications, 2009
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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
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Problem With Critical Sobolev Exponent and With Potential on SN

Journal of Applied Mathematics
We consider the equation −divSNqx∇Snu=u2∗−1,u>0 in D’, u=0 on D′, where D′ is a geodesic ball with radius θ1, centered at the north pole, on SN, N≥4, and q is a positive continuous function.
Walid Refai, Habib Yazidi
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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
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