Results 151 to 160 of about 406 (185)

On Elliptic System Involving Critical Sobolev Exponent and Weights

Mediterranean Journal of Mathematics, 2013
From the authors' abstract: This paper is devoted to the existence and nonexistence of positive solutions for a semilinear elliptic system involving critical Sobolev exponent and weights. We study the effect of the behavior of weights near their minima on the existence of solutions for the considered problem.
Bouchekif, Mohammed, Hamzaoui, Yamina
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p-Laplacian problems with critical Sobolev exponent

Asymptotic Analysis, 2011
We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical non-linearity in general, possibly non-smooth, bounded domains.
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On Nonlocal Choquard System with Hardy–Littlewood–Sobolev Critical Exponents

The Journal of Geometric Analysis, 2022
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Luo, Xiaorong, Mao, Anmin, Mo, Shuai
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A quasilinear elliptic problem involving critical Sobolev exponents

Collectanea Mathematica, 2014
The authors study a quasilinear elliptic equation of the form \[ \begin{cases} -\Delta_p u = |u|^{p^*-2}u+g(u), & \text{in } \Omega,\\ u=0, & \text{on }\partial \Omega, \end{cases} \] where \(\Omega\) is a bounded domain of \(\mathbb{R}^N\) with smooth boundary \(\partial\Omega\), \(1 < p < N\), \(\Delta_p\) is the \(p\)-Laplace operator, that is ...
FARACI, FRANCESCA, FARKAS Cs
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A Note on Elliptic Equations Involving the Critical Sobolev Exponent

2013
In this work we obtain some existence results for a class of elliptic Dirichlet problems involving the critical Sobolev exponent and containing a parameter. Through a weak lower semicontinuity result and by using a critical point theorem for differentiable functionals, the existence of a precise open interval of positive eigenvalues for which the ...
BONANNO, Gabriele, G. Molica Bisci, V. Radulescu   +2 more
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Existence of solutions for elliptic equations with critical Sobolev–Hardy exponents

Nonlinear Analysis: Theory, Methods & Applications, 2004
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Kang, Dongsheng, Peng, Shuangjie
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A minimization problem on RN involving critical Sobolev exponent

Nonlinear Analysis: Theory, Methods & Applications, 1992
The authors develop some technical ideas in order to treat the minimization problem: \[ \inf\left\{\int_{R^ N} a_{ij}(u)D_ i uD_ j u\left| u\in{\mathcal D}^{1,2}(R^ N),\right.\int_{R^ N}| u|^{2^*}=1\right\}, \] where \(2^*=2N/(N-2)\), \(N\geq 3\). By analysing carefully the minimizing sequence, the authors define the corresponding minimization problem ...
Yan, Shusen, Zhang, Zhengjie
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On Kirchhoff type equations with critical Sobolev exponent

Journal of Mathematical Analysis and Applications, 2018
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Yisheng Huang, Zeng Liu, Yuanze Wu
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Normalized Solutions of the Choquard Equation with Sobolev Critical Exponent

Frontiers of Mathematics
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Feng, Xiaojing, Li, Yuhua
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ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT

Bulletin of the London Mathematical Society, 2005
Summary: In this paper, the existence problem is studied for extremals of the Sobolev trace inequality \(W^{1,p}(\Omega)\hookrightarrow L^{p^*}(\partial\Omega)\), where \(\Omega\) is a bounded smooth domain in \(\mathbb R^N\), \(p^*=p(N-1)/(N-p)\), is the critical Sobolev exponent, and \(1< p < N\).
Bonder, JF, Rossi, JD
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