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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Non-homogeneous problem for fractional Laplacian involving critical Sobolev exponent
Electronic Journal of Differential Equations, 2017 In this article, we study the existence of positive solutions for the nonhomogeneous fractional equation involving critical Sobolev exponent $$\displaylines{ (-\Delta)^{s} u +\lambda u=u^p+\mu f(x), \quad u>0\quad \text{in } \Omega,\cr u =0, \quad \
Kun Cheng, Li Wang
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Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight
Electronic Journal of Differential Equations, 2016 In this article we consider the problem $$\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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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 EquationsWe 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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On singular elliptic equation with singular nonlinearities, Hardy-Sobolev critical exponent and weights [PDF]
, 2020 Mohammed El Mokhtar Ould El Mokhtar +1 more
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Quasilinear elliptic problems involving multiple critical Hardy–Sobolev exponents
Computers & Mathematics with Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Existence and multiplicity for perturbations of an equation involving a Hardy inequality and the critical Sobolev exponent in the whole of $\Bbb R^N$ [PDF]
, 2004 Boumediene Abdellaoui +2 more
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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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