Results 21 to 30 of about 4,702,923 (209)

A system with weights and with critical Sobolev exponent

European Journal of Mathematics, 2023
In this paper, we investigate the minimization problem : $$ \inf_{ \displaystyle{\begin{array}{lll} u \in H_0^1(Ω), v \in H_0^1(Ω),\\ \quad \| u \|_{L^{q}} =1, \quad \| v \|_{L^{q}} = 1 \end{array}}} \left[ \frac{1}{2} \int_Ω a(x) \vert \nabla u(x) \vert^2dx + \displaystyle{ \frac{1}{2} \int_Ω b(x) \vert \nabla v (x)\vert^2dx } - λ\displaystyle{\int_Ω ...
Benhamida, Asma, Hadiji, Rejeb
openaire   +2 more sources

Weighted critical exponents of Sobolev-type embeddings for radial functions

Advanced Nonlinear Studies, 2022
In this article, we prove the upper weighted critical exponents for some embeddings from weighted Sobolev spaces of radial functions into weighted Lebesgue spaces. We also consider the lower critical exponent for certain embedding.
Su Jiabao, Wang Cong
doaj   +1 more source

On Hamiltonian systems with critical Sobolev exponents

Journal of Differential Equations, 2023
26 ...
Angelo Guimarães, Ederson Moreira dos Santos   +1 more
openaire   +3 more sources

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, Atika Matallah, Safia Benmansour, Mohammed El Mokhtar Ould El Mokhtar   +3 more
doaj   +1 more source

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
openaire   +3 more sources

Ground State Solutions for the Nonlinear Schrödinger–Bopp–Podolsky System with Critical Sobolev Exponent

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
doaj   +1 more source

Nonhomogeneous elliptic problems of Kirchhoff type involving critical Sobolev exponents

Electronic Journal of Differential Equations, 2015
This article concerns the existence and the multiplicity of solutions for nonhomogeneous elliptic Kirchhoff problems involving the critical Sobolev exponent, defined on a regular bounded domain of $\mathbb{R}^3$.
Safia Benmansour, Mohammed Bouchekif
doaj   +1 more source

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
doaj   +1 more source

Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space

Electronic Journal of Differential Equations, 2022
In this work we study a class of the critical Kirchhoff-type problems in a Hyperbolic space Because of the Kirchhoff term, the nonlinearity \(u^q\) becomes concave for ...
Paulo Cesar Carriao, Augusto Cesar dos Reis Costa, Olimpio Hiroshi Miyagaki, Andre Vicente   +3 more
doaj   +1 more source

Semilinear elliptic partial differential equations with the critical Sobolev exponent [PDF]

, 2017
We present how variational methods and results from linear and non-linear functional analysis are applied to solving certain types of semilinear elliptic partial differential equations (PDEs).
Mavuso, Melusi Manqoba
core   +1 more source