Results 41 to 50 of about 745 (91)

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

Positive solutions for the fractional Schrödinger equations with logarithmic and critical non‐linearities

Transactions of the London Mathematical Society, 2021
In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ...
Haining Fan, Zhaosheng Feng, Xingjie Yan
doaj   +1 more source

Positive solutions to p-Laplace reaction-diffusion systems with nonpositive right-hand side [PDF]

, 2015
The aim of the paper is to show the existence of positive solutions to the elliptic system of partial differential equations involving the $p$-Laplace operator\[\begin{cases}-\Delta_p u_i(x) = f_i(u_1 (x),u_2(x),\ldots,u_m(x)), & x\in \Omega,\ 1\leq ...
Maciejewski, Mateusz
core   +1 more source

Ground State for a Coupled Elliptic System with Critical Growth

Advanced Nonlinear Studies, 2018
We study the following coupled elliptic system with critical nonlinearities:
Wu Huiling, Li Yongqing
doaj   +1 more source

Radially symmetric solutions to the Hènon-Lane-Emden system on the critical hyperbola [PDF]

, 2013
We use variational methods to study the existence of nontrivial and radially symmetric solutions to the H\`enon-Lane-Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative properties of solutions and nonexistence results.
arxiv   +1 more source

Positive multipeak solutions to a zero mass problem in exterior domains

, 2018
We establish the existence of positive multipeak solutions to the nonlinear scalar field equation with zero mass $$-\Delta u = f(u), \qquad u\in D_0^{1,2}(\Omega_R),$$ where $\Omega_R:=\{x \in \mathbb{R}^N:|u|>R\}$ with $R>0$, $N\geq4$, and the ...
Clapp, Mónica, Maia, Liliane A., Pellacci, Benedetta   +2 more
core   +1 more source

Existence of Ground States of Fractional Schrödinger Equations

Advanced Nonlinear Studies, 2021
We consider ground states of the nonlinear fractional Schrödinger equation with ...
Ma Li, Li Zhenxiong
doaj   +1 more source

Increasing powers in a degenerate parabolic logistic equation [PDF]

, 2012
The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \partial_t u-\Delta u=a u-b(x) u^p \text{in} \Omega\times \R^+, u(0)=u_0, u(t)|_{\partial \Omega}=0 $$ as $p\to +\infty$, where $\Omega$ is a ...
Hugo Tavares, Jose Francisco, Rodrigues
core  

Supercritical Hénon-type equation with a forcing term

Advances in Nonlinear Analysis
This article is concerned with the structure of solutions to the elliptic problem for a Hénon-type equation with a forcing term: −Δu=α(x)up+κμ,inRN,u>0,inRN,(Pκ)\hspace{11.3em}-\Delta u=\alpha \left(x){u}^{p}+\kappa \mu ,\hspace{1.0em}\hspace{0.1em}\text{
Ishige Kazuhiro, Katayama Sho
doaj   +1 more source

The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

Advanced Nonlinear Studies
The existence of L 2–normalized solutions is studied for the equation −Δu+μu=f(x,u)  inRN,∫RNu2dx=m. $-{\Delta}u+\mu u=f\left(x,u\right)\quad \quad \text{in} {\mathbf{R}}^{N},\quad {\int }_{{\mathbf{R}}^{N}}{u}^{2} \mathrm{d}x=m.$ Here m > 0 and f(x, s)
Ikoma Norihisa, Yamanobe Mizuki
doaj   +1 more source