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Science China Mathematics 2020年第7期63卷 1307-1322页

作者： Huyuan Chen Rui Peng Feng Zhou Department of Mathematics Jiangxi Normal UniversityNanchang 330022China School of Mathematics and Statistics Jiangsu Normal UniversityXuzhou 221116China Center for PDEs and School of Mathematical Sciences East China Normal UniversityShanghai 200241China

In this paper,we consider the following semilinear elliptic equation:■whereΩis an exterior domain in R^N with N≥3,h:Ω×R^+→R is a measurable function,and derive optimal nonexistence results of positive *** argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy *** also establish sharp nonexistence results of positive supersolutions to an elliptic system.

关键词： semilinear elliptic problem supersolution nonexistence

nonexistence AND SYMMETRY OF SOLUTIONS TO SOME FRACTIONAL LAPLACIAN EQUATIONS IN THE UPPER HALF SPACE

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Acta Mathematica Scientia 2017年第3期37卷 836-851页

作者：郭艳艳 Department of Applied Mathematics Northwestern Polytechnical UniversityXi'an 710129China

In this article, we consider the fractional Laplacian equation {（-△）α/2u=k（x）f（u）,x∈Rn＋, u=0, x Rn＋, where 0 〈α 〈 2,En＋：= {x = （x1,x2,… ,xn）｜xn〉 0}. When K is strictly decreasing with respect to ｜x＇｜, the symmetry of positive solutions is proved, where x＇ = （x1, x2,…, xn-1） ∈Rn- 1. When K is strictly increasing with respect to xn or only depend on xn, the nonexistence of positive solutions is obtained.

关键词： Fractional Laplacian method of moving planes radial symmetry nonexistence

nonexistence and Longtime Behaviors of Solutions to a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 327-332页

作者： Yu-dong SUN Yi-min SHI MIN WU School of Science Guizhou Minzu University Department of Applied Mathematics Northwestern Polytechnical University

In this paper, we study the nonexistence and longtime behavior of weak solution for the degenerate parabolic equation σtun=umdiv（｜▽um｜p-2▽um）＋γ｜▽um｜p＋βun with zero boundary condition. Blow-up time is der... 详细信息

关键词： nonexistence nonlinear degenerate parabolic equations weak solution blow-up

Existence and nonexistence of Nontrivial Weak Solution for a Class of General Capillarity Systems

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Acta Mathematicae Applicatae Sinica 2014年第4期30卷 1121-1130页

作者： G.A.AFROUZI N.T.CHUNG Z.NAGHIZADEH Department of Mathematics Faculty of Mathematical SciencesUniversity of Mazandaran Department of Mathematics Quang Binh University312 Ly Thuong Kiet

The aim of this paper is to study the nonexistence and existence of nonnegative, nontrivial weak solution for a class of general capillarity systems. The proofs rely essentially on the minimum principle combined with ... 详细信息

关键词： weak solutions nonexistence multiplicity capillarity systems variational methods

GLOBAL nonexistence FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2020年第1期40卷 155-169页

作者：于佳利尚亚东狄华斐 School of Science Dalian Jiaotong UniversityDalian 116028China School of Mathematics and Information Science Guangzhou UniversityGuangzhou 510006China

This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms utt-Δu-Δut-Δutt+∫^t0g(t-s)Δu(s)ds+ut|ut|^m2-=u|u|^p-2 with acoustic boundary *** some appropriate assumption on relaxation function g and the initial data,we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

关键词： viscoelastic wave equation Global nonexistence Acoustic boundary conditions

A nonexistence Result for Choquard-Type Hamiltonian System

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Journal of Applied Mathematics and Physics 2023年第3期11卷 608-617页

作者： Zexi Wang School of Mathematics and Statistics Southwest University Chongqing China

In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity , when , , , , , and , where and denotes the convolu... 详细信息

关键词： nonexistence Choquard-Type Hamiltonian System Pohožaev Identity

EXISTENCE AND nonexistence OF GLOBAL SOLUTIONS FOR A SEMI-LINEAR HEAT EQUATION WITH FRACTIONAL LAPLACIAN

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Acta Mathematica Scientia 2012年第6期32卷 2203-2210页

作者：谭忠许勇强 School of Mathematical Sciences Xiamen University Fujian Department of Mathematics and Information Sciences Zhangzhou Normal University

In this paper, we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian. We obtain some extem sion of results of Weissler who considered the ca... 详细信息

关键词： fractional Laplacian equation global existence nonexistence

The nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption

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Journal of Partial Differential Equations 2021年第4期34卷 369-378页

作者： OU Qitong School of Applied Mathematics Xiamen University of TechnologyXiamen 361024China

The paper proves the nonexistence of the solution for the following Cauchy problem{ut=div(|■u^m|(p-2■u^(m)))^-λu^(q),u(x,0)=δ(x),(x,t)∈S_(T)=R^(N)×(0,T),x∈R^(N),under some conditions on m,p,q,λ,whereδis Dirac... 详细信息

关键词： Non-Newtonian filtration equation Cauchy problem nonexistence

nonexistence of Nontrivial Solutions with Decay Order for a Biharmonic P-Laplacian Equation and System

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Applied Mathematics 2017年第7期8卷 920-928页

作者： Jeng-Eng Lin Department of Mathematics and Statistics Georgetown University Washington DC USA

We use the Morawetz multiplier to show that there are no nontrivial solutions of certain decay order for a biharmonic equation with a p-Laplacian term and a system of coupled biharmonic equations with p-Laplacian term... 详细信息

关键词： Morawetz Multiplier Biharmonic P-Laplacian nonexistence

The nonexistence of Global Solutions for a Time Fractional Schrodinger Equation with Nonlinear Memory

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Journal of Applied Mathematics and Physics 2018年第7期6卷 1418-1424页

作者： Yaning Li Quanguo Zhang College of Mathematics&Statistics Nanjing University of Information Science&TechnologyNanjingChina Department of Mathematics Luoyang Normal UniversityLuoyangHenanChina

In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}, u(t,x) is a complex-value function, denotes left Riemann-Liouville fractional integrals of order 1-λ and is the Caputo fractional derivative of order . We obtain that the problem admits no global weak solution when and under different conditions for initial data.

关键词： Fractional Schrodinger Equation nonexistence Cauchy Problems Nonlinear Memory