Results 11 to 20 of about 406 (185)

Inhomogeneous Neumann problem with critical Sobolev exponent [PDF]

Advances in Nonlinear Analysis, 2012
We investigate the solvability of the inhomogeneous Neumann problem involving the critical Sobolev exponent. In particular, we discuss the impact of the shape of the graph of the coefficient of the critical exponent on the existence of a solution.
Chabrowski Jan
doaj   +4 more sources

Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent [PDF]

Journal of Inequalities and Applications, 2017
In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term.
Yanbin Sang, Siman Guo
doaj   +2 more sources

Problem With Critical Sobolev Exponent and With Potential on SN

Journal of Applied Mathematics
We consider the equation −divSNqx∇Snu=u2∗−1,u>0 in D’, u=0 on D′, where D′ is a geodesic ball with radius θ1, centered at the north pole, on SN, N≥4, and q is a positive continuous function.
Walid Refai, Habib Yazidi
doaj   +2 more sources

Toward the theory of the Sobolev classes with critical exponent

Доповiдi Нацiональної академiї наук України, 2019
It is established that an arbitrary homeomorphism f in the Sobolev class W1,n−1loc with the outer dilatation K0(x,f)∈Ln−1loc is the socalled lower Q - homeomorphism with Q=K0(x,f) and the ring Q* homeomorphism with Q∗=Kn−10(x,f).
O.S. Afanas’eva, V.I. Ryazanov, R.R. Salimov   +2 more
doaj   +2 more sources

On a singular nonlinear Neumann problem [PDF]

Opuscula Mathematica, 2014
We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text ...
Jan Chabrowski
doaj   +1 more source

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
openaire   +5 more sources

Existence of solution for a quasilinear elliptic Neumann problem involving multiple critical exponents

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
doaj   +1 more source

Groundstates for Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical exponent

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
doaj   +1 more source

On a semilinear Schrödinger equation with critical Sobolev exponent [PDF]

Proceedings of the American Mathematical Society, 2001
We consider the semilinear Schrödinger equation − Δ
Chabrowski, Jan, Szulkin, Andrzej
openaire   +5 more sources

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