Results 21 to 30 of about 1,238 (226)

On a Minimization Problem Involving the Critical Sobolev Exponent

Advanced Nonlinear Studies, 2007
Abstract Following [3] we study the following minimization problem: in any dimension n ≥ 4 and under suitable assumptions on a(x).
PRINARI F, VISCIGLIA, NICOLA
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Existence and concentration behavior of solutions for a class of quasilinear elliptic equations with critical growth

Advances in Nonlinear Analysis, 2017
In this paper, we study a class of quasilinear elliptic equations involving the Sobolev critical ...
Teng Kaimin, Yang Xiaofeng
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Normalized solutions for nonlinear Kirchhoff type equations in high dimensions

Electronic Research Archive, 2022
We study the normalized solutions for nonlinear Kirchhoff equation with Sobolev critical exponent in high dimensions $ \mathbb{R}^N(N\geqslant4) $. In particular, in dimension $ N = 4 $, there is a special phenomenon for Kirchhoff equation that the mass ...
Lingzheng Kong, Haibo Chen
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Schrödinger equation with critical Sobolev exponent

Differential and Integral Equations, 2004
In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.
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A singular perturbed problem with critical Sobolev exponent

Topological Methods in Nonlinear Analysis, 2021
This paper deals with the following nonlinear elliptic problem \begin{equation}\label{eq0.1} -\varepsilon^2\Delta u+\omega V(x)u=u^{p}+u^{2^{*}-1},\quad u> 0\quad\text{in}\ \R^N, \end{equation} where $\omega\in\R^{+}$, $N\geq 3$, $p\in (1,2^{*}-1)$ with $2^{*}={2N}/({N-2})$, $\varepsilon> 0$ is a small parameter and $V(x)$ is a given function ...
Mengyao Chen, Qi Li
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Existence Results for Singular p-Biharmonic Problem with HARDY Potential and Critical Hardy-Sobolev Exponent

Axioms
In this article, we consider the singular p-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold ...
Gurpreet Singh
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$p$-Laplacian problems involving critical Hardy-Sobolev exponents

, 2016
arXiv admin note: text overlap with arXiv:1602.01071, arXiv:1407.4505, arXiv:1406 ...
Perera, Kanishka, Zou, Wenming
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A Nonlinear Elliptic PDE with Two Sobolev–Hardy Critical Exponents [PDF]

Archive for Rational Mechanics and Analysis, 2011
In this paper, we consider the following PDE involving two Sobolev-Hardy critical exponents, \label{0.1} {& u + \frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \text{in} , & u=0 \qquad \text{on} , where $0 \le s_2 < s_1 \le 2$, $0 \ne \in \Bbb R$ and $0 \in \partial $.
Li, YanYan, Lin, Chang-Shou
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A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN

Advanced Nonlinear Studies, 2017
This paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent:
Xiang Mingqi, Zhang Binlin, Zhang Xia
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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

Advances in Nonlinear Analysis, 2020
We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
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