Results 21 to 30 of about 440,485 (323)

Nonlinear elliptic boundary value problems with convection term and Hardy potential

Moroccan Journal of Pure and Applied Analysis, 2023
In this paper, we deal with a nonlinear elliptic problems that incorporate a Hardy potential and a nonlinear convection term. We establish the existence and regularity of solutions under various assumptions concerning the summability of the source term f.
Achhoud Fessel, Bouajaja Abdelkader, Redwan Hicham   +2 more
doaj   +1 more source

Infinitely many solutions for a quasilinear Schrödinger equation with Hardy potentials

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this article, we study the following quasilinear Schr\"odinger equation \begin{equation*} -\Delta u-\mu\frac{u}{|x|^{2}}+V(x)u-(\Delta(u^{2}))u=f(x,u),\qquad x\in \mathbb{R}^{N}, \end{equation*} where $ V(x) $ is a given positive potential and the ...
Tingting Shang, Ruixi Liang
doaj   +1 more source

On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain

Advances in Nonlinear Analysis, 2021
We study the wave inequality with a Hardy ...
Jleli Mohamed, Samet Bessem, Vetro Calogero   +2 more
doaj   +1 more source

On Scales of Sobolev spaces associated to generalized Hardy operators

, 2021
We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized and reversed Hardy inequalities, the analysis relies on a H\"ormander multiplier theorem ...
Merz, Konstantin
core   +1 more source

A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain

Mathematics, 2023
A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of RN, is considered under a Dirichlet boundary condition.
Bessem Samet, Calogero Vetro
doaj   +1 more source

Restricting Riesz–Morrey–Hardy potentials

Journal of Differential Equations, 2017
This paper concerns the study of continuity of the Riesz operator \(I_\alpha\) of order \(\alpha\) between the Morey-Hardy space \(LH^{p,\kappa}\) and the Morey-Radon space \(L_\mu^{q,\lambda}\). More precisely, the main result established is the following.
Liu, Liguang, Xiao, Jie
openaire   +1 more source

Semilinear heat equation with singular terms

Electronic Journal of Qualitative Theory of Differential Equations, 2022
The main goal of this paper is to analyze the existence and nonexistence as well as the regularity of positive solutions for the following initial parabolic problem $$ \begin{cases} \partial_tu-\Delta u=\displaystyle\mu\frac{u}{|x|^{2}}+\frac{f}{u ...
Mohamed Mahmoud Ould Khatri, Ahmed Youssfi   +1 more
doaj   +1 more source

On nonhomogeneous elliptic equations with the Hardy—Leray potentials [PDF]

Journal d'Analyse Mathématique, 2021
In this paper, we present some suitable distributional identities of the solutions for nonhomogeneous elliptic equations involving the Hardy-Leray potentials and study qualitative properties of the solutions to the corresponding nonhomogeneous problems by the distributional identities.
Chen, Huyuan, Quaas, Alexander, Zhou, Feng   +2 more
openaire   +2 more sources

Improved Poincar\'e inequalities [PDF]

, 2011
Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic
Dolbeault, Jean, Volzone, Bruno
core   +2 more sources

Fractional KPZ equations with fractional gradient term and Hardy potential

Mathematics in Engineering, 2023
In this work we address the question of existence and non existence of positive solutions to a class of fractional problems with non local gradient term. More precisely, we consider the problem $ \left\{ \begin{array}{rcll} (-\Delta )^s u & = &
Boumediene Abdellaoui, Kheireddine Biroud, Ana Primo, Fernando Soria, Abdelbadie Younes   +4 more
doaj   +1 more source