Results 1 to 10 of about 14,354,842 (233)

Nonlocal problems at critical growth in contractible domains [PDF]

Asymptotic Analysis, 2015
We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.Comment: 17 ...
Mosconi, Sunra, Shioji, Naoki, Squassina, Marco   +2 more
core   +2 more sources

Slip Line Growth as a Critical Phenomenon

Physical Review Letters, 2009
We study the growth of slip line in a plastically deforming crystal by numerical simulation of a double-ended pile-up model with a dislocation source at one end, and an absorbing wall at the other end. In presence of defects, the pile-up undergoes a second order non-equilibrium phase transition as a function of stress, which can be characterized by ...
Fabio Leoni, Stefano Zapperi
openaire   +5 more sources

Ground states for a fractional scalar field problem with critical growth [PDF]

Differential and Integral Equations, 2016
We prove the existence of a ground state solution for the following fractional scalar field equation $(-\Delta)^{s} u= g(u)$ in $\mathbb{R}^{N}$ where $s\in (0,1), N> 2s$,$ (-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}(\mathbb{R ...
Ambrosio, Vincenzo
core   +2 more sources

Normalized Ground State Solutions of Nonlinear Schrödinger Equations Involving Exponential Critical Growth [PDF]

Journal of Geometric Analysis, 2022
We are concerned with the following nonlinear Schrödinger equation: $$\begin{aligned} \begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+\lambda u=f(u) \ \ \textrm{in}\ \mathbb {R}^{2},\\ u\in H^{1}(\mathbb {R}^{2}),~~~ \int _{\mathbb {R}^2}u^2dx=\rho ,
Xiaojun Chang, Man Liu, Duokui Yan
semanticscholar   +1 more source

Parametric superlinear double phase problems with singular term and critical growth on the boundary [PDF]

Mathematical methods in the applied sciences, 2021
In this paper, we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has a singular and a parametric superlinear term and with a nonlinear Neumann boundary condition of critical growth.
Ángel Crespo-Blanco, N. Papageorgiou, Patrick Winkert   +2 more
semanticscholar   +1 more source

Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth

AIMS Mathematics, 2021
In this paper, we consider a Neumann problem of Kirchhoff type equation \begin{equation*} \begin{cases} \displaystyle-\left(a+b\int_{\Omega}|\nabla u|^2dx\right)\Delta u+u= Q(x)|u|^4u+\lambda P(x)|u|^{q-2}u, &\rm \mathrm{in}\ \ \Omega ...
Jun Lei, Hongmin Suo
doaj   +1 more source

A planar Schrödinger–Newton system with Trudinger–Moser critical growth

Calculus of Variations and Partial Differential Equations, 2023
In this paper, we focus on the existence of positive solutions to the following planar Schrödinger–Newton system with general critical exponential growth $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta {u}+u+\phi u =f(u)&{} \text{ in }\,\,\mathbb {R}^
Zhisu Liu, V. Rǎdulescu, Jianjun Zhang
semanticscholar   +1 more source

Critical Growth Phases for Adult Shortness [PDF]

American Journal of Epidemiology, 2000
Previous growth studies have not explored how different growth phases-the fetal, infancy, childhood, and puberty phases-interact with each other in the development of adult shortness. In this paper, the authors attempt to describe the importance of each growth phase for adult shortness and the effect of growth in one phase on other, subsequent phases ...
Luo, ZC, Karlberg, J
openaire   +4 more sources

On sufficient “local” conditions for existence results to generalized p(.)-Laplace equations involving critical growth

Advances in Nonlinear Analysis, 2022
In this article, we study the existence of multiple solutions to a generalized p(⋅)p\left(\cdot )-Laplace equation with two parameters involving critical growth.
Ho Ky, Sim Inbo
doaj   +1 more source

Critical transitions and perturbation growth directions [PDF]

Physical Review E, 2017
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical
Sharafi, N., Timme, M., Hallerberg, S.
openaire   +5 more sources