Results 41 to 50 of about 1,283 (108)

On the singularly perturbation fractional Kirchhoff equations: Critical case

Advances in Nonlinear Analysis, 2022
This article deals with the following fractional Kirchhoff problem with critical exponent a+b∫RN∣(−Δ)s2u∣2dx(−Δ)su=(1+εK(x))u2s∗−1,inRN,\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{N}}| {\left(-\Delta )}^{\tfrac{s}{2}}u\hspace{-0.25em}{| }^{2}{\rm{d ...
Gu Guangze, Yang Zhipeng
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Generalized Picone inequalities and their applications to (p,q)-Laplace equations

Open Mathematics, 2020
We obtain a generalization of the Picone inequality which, in combination with the classical Picone inequality, appears to be useful for problems with the (p,q)(p,q)-Laplace-type operators.
Bobkov Vladimir, Tanaka Mieko
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Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian

Advanced Nonlinear Studies
In the present paper, we study the well-posedness of the solution to the initial boundary value problem for the damped Kirchhoff-type wave equation with fractional Laplacian.
Chen Shaohua, Han Jiangbo, Xu Runzhang, Yang Chao, Zhang Meina   +4 more
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Qualitative properties of two-end solutions to the Allen–Cahn equation in R3 ${\mathbb{R}}^{3}$

Advanced Nonlinear Studies
A solution of the Allen–Cahn equation in R3 ${\mathbb{R}}^{3}$ is called a two-end solution if its nodal set is asymptotic to (x′,z)∈R3:z=ki⁡ln|x′|+ci,1≤i≤2 $\left\{\left({x}^{\prime },z\right)\in {\mathbb{R}}^{3}:z={k}_{i}\mathrm{ln}\vert {x}^{\prime }\
Liang Weizhao, Yang Jianmin
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Qualitative properties of solutions to the viscoelastic beam equation with damping and logarithmic nonlinear source terms

Advances in Nonlinear Analysis
In this article, we consider the initial-boundary value problem for a class of viscoelastic extensible beam equations with logarithmic source term, strong damping term, and weak damping term.
Gao Yanchao, Pan Bingbai
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A Blow-Up Criterion for the 3D Euler Equations Via the Euler-Voigt Inviscid Regularization

, 2015
We propose a new blow-up criterion for the 3D Euler equations of incompressible fluid flows, based on the 3D Euler-Voigt inviscid regularization. This criterion is similar in character to a criterion proposed in a previous work by the authors, but it is ...
Larios, Adam, Titi, Edriss S.
core  

Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks

Advances in Nonlinear Analysis
The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the ...
Li Bin
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On isolated singularities of Kirchhoff equations

Advances in Nonlinear Analysis, 2020
In this note, we study isolated singular positive solutions of Kirchhoff ...
Chen Huyuan, Fall Mouhamed Moustapha, Zhang Binling   +2 more
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Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems

Open Mathematics, 2020
The aim of this paper is to investigate a class of nonlinear stochastic reaction-diffusion systems involving fractional Laplacian in a bounded domain. First, the existence and uniqueness of weak solutions are proved by using Galërkin’s method.
Fu Yongqiang, Yan Lixu
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Variations in the geometry of the basins of escape in a modified Hénon–Heiles potential

Demonstratio Mathematica
In this article, we show how the curves that limit the basins of escape in a version of a Hénon–Heiles potential with a singularity at the origin evolve with the energy.
Navarro Juan F.
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