Results 11 to 20 of about 1,238 (226)
Boundary Value Problems, 2020 In this paper, we study the Neumann boundary value problem to a quasilinear elliptic equation with the critical Sobolev exponent and critical Hardy–Sobolev exponent, and prove the existence of nontrivial nonnegative solution by means of variational ...
Yuanxiao Li, Xiying Wang
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Problem with Critical Sobolev Exponent and with Weight [PDF]
Chinese Annals of Mathematics, Series B, 2007 We study existence results for a problem with criticical Sobolev exponent and with a positive weight.
Hadiji, Rejeb, Yazidi, Habib
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Advances in Nonlinear Analysis, 2021 We are concerned with a class of Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical ...
Zhou Shuai, Liu Zhisu, Zhang Jianjun
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Strongly indefinite systems with critical Sobolev exponents [PDF]
Transactions of the American Mathematical Society, 1998 Let \(\Omega\) be a bounded domain in \(\mathbb R^n\) (\(n\geq 4\)) with smooth boundary, \(\lambda, \mu\in\mathbb R\), and \(p\geq q>1\). The authors investigate the solvability of the system \[ -\Delta v=\lambda u+| u|^{p-1}u,\quad -\Delta u=\mu v+| v|^{q-1}v\quad \text{in } \Omega,\qquad u=0=v\quad\text{on }\partial\Omega, \] in case that \({1\over ...
MITIDIERI, ENZO +2 more
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Existence of Two Solutions for a Critical Elliptic Problem with Nonlocal Term in ℝ4
Journal of Function Spaces, 2022 In this paper, we prove the existence of two positive solutions for a critical elliptic problem with nonlocal term and Sobolev exponent in dimension four.
Khadidja Sabri +3 more
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On a p-Laplacian system with critical Hardy–Sobolev exponents and critical Sobolev exponents [PDF]
Ukrainian Mathematical Journal, 2012 In this paper, the existence results of positive solutions for the semiliner elliptic system \[ \begin{cases} -\text{div} (|\nabla u_i|^{p-2} \nabla u_i) - \mu \frac{|u_i|^{p-2}u_i}{|x|^p} \\ = \frac{1}{p^*} F_{u_i}(u_1,\ldots,u_k) + \frac{|u_i|^{p^*(t)-2}u_i}{|x|^t} + \lambda \frac{|u_i|^{p-2}u_i}{|x|^s}, \quad x \in \Omega, \\ u_i=0 \quad \text{on} \;
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Advanced Nonlinear Studies, 2020 In this paper, we study the existence of ground state solutions for the nonlinear Schrödinger–Bopp–Podolsky system with critical Sobolev ...
Li Lin, Pucci Patrizia, Tang Xianhua
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The Existence Result for a p-Kirchhoff-Type Problem Involving Critical Sobolev Exponent
Journal of Function Spaces, 2023 In this paper, by using the mountain pass theorem and the concentration compactness principle, we prove the existence of a positive solution for a p-Kirchhoff-type problem with critical Sobolev exponent.
Hayat Benchira +3 more
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
Advances in Nonlinear Analysis, 2020 It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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Fractional Laplacian equations with critical Sobolev exponent [PDF]
Revista Matemática Complutense, 2015 The paper under review extends in a fractional setting some results concerning the existence of nontrivial solutions for a class of nonlocal elliptic Dirichlet problems involving critical nonlinear terms. The basic analytic tool to establish the existence of a nontrivial solution is the linking method.
R. Servadei, E. Valdinoci
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