Results 31 to 40 of about 741 (89)

Classification of solutions to $Δu = u^{-γ}$ in the half-space [PDF]

arXiv, 2023
We provide a classification result for positive solutions to $\Delta u = u^{-\gamma}$ in the half space, under zero Dirichlet boundary condition.
arxiv  

Existence and uniqueness of a positive solution to generalized nonlocal thermistor problems with fractional-order derivatives

, 2011
In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and uniqueness of a positive solution.Comment: Submitted 17-Jul-2011; revised 09-Oct-
Ammi, Moulay Rchid Sidi, Torres, Delfim F. M.   +1 more
core   +1 more source

Ground states of Schrödinger systems with the Chern-Simons gauge fields

Advanced Nonlinear Studies, 2023
We are concerned with the following coupled nonlinear Schrödinger system: −Δu+u+∫∣x∣∞h(s)su2(s)ds+h2(∣x∣)∣x∣2u=∣u∣2p−2u+b∣v∣p∣u∣p−2u,x∈R2,−Δv+ωv+∫∣x∣∞g(s)sv2(s)ds+g2(∣x∣)∣x∣2v=∣v∣2p−2v+b∣u∣p∣v∣p−2v,x∈R2,\left\{\begin{array}{l}-\Delta u+u+\left(\underset{|
Jiang Yahui, Chen Taiyong, Zhang Jianjun, Squassina Marco, Almousa Nouf   +4 more
doaj   +1 more source

Supersolutions to nonautonomous Choquard equations in general domains

Advances in Nonlinear Analysis, 2023
We consider the nonlocal quasilinear elliptic problem: −Δmu(x)=H(x)((Iα*(Qf(u)))(x))βg(u(x))inΩ,-{\Delta }_{m}u\left(x)=H\left(x){(\left({I}_{\alpha }* \left(Qf\left(u)))\left(x))}^{\beta }g\left(u\left(x))\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0 ...
Aghajani Asadollah, Kinnunen Juha
doaj   +1 more source

A note on higher order fractional Hardy-Sobolev inequalities [PDF]

arXiv, 2020
We establish some qualitative properties of minimizers in the fractional Hardy--Sobolev inequalities of arbitrary order.
arxiv  

Ground states of nonlocal scalar field equations with Trudinger-Moser critical nonlinearity

, 2015
We investigate the existence of ground state solutions for a class of nonlinear scalar field equations defined on whole real line, involving a fractional Laplacian and nonlinearities with Trudinger-Moser critical growth. We handle the lack of compactness
Miyagaki, Olímpio H., Squassina, Marco, Ó, João Marcos do   +2 more
core   +1 more source

Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions

Advances in Nonlinear Analysis
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term is sign ...
Díaz Jesús Ildefonso, Hernández Jesús   +1 more
doaj   +1 more source

Existence and uniqueness results for a fractional Riemann–Liouville nonlocal thermistor problem on arbitrary time scales

Journal of King Saud University: Science, 2018
Using a fixed point theorem in a proper Banach space, we prove existence and uniqueness results of positive solutions for a fractional Riemann–Liouville nonlocal thermistor problem on arbitrary nonempty closed subsets of the real numbers.
Moulay Rchid Sidi Ammi, Delfim F.M. Torres   +1 more
doaj  

Existence and non-degeneracy of the normalized spike solutions to the fractional Schrödinger equations

Advances in Nonlinear Analysis
The present study investigates the existence and non-degeneracy of normalized solutions for the following fractional Schrödinger equation: (−Δ)su+V(x)u=aup+μu,x∈RN,u∈Hs(RN){\left(-\Delta )}^{s}u+V\left(x)u=a{u}^{p}+\mu u,\hspace{1.0em}x\in {{\mathbb{R}}}^
Guo Qing, Zhang Yuhang
doaj   +1 more source

On some strong ratio limit theorems for heat kernels

, 2010
We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.Comment: 16 pages.
Fraas, M., Krejcirik, D., Pinchover, Y.
core   +1 more source