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The Solutions with Prescribed asymptotic behavior for the Exterior Dirichlet Problem of Hessian Equations

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Analysis in Theory and Applications 2023年第2期39卷 120-146页

作者： Limei Dai School of Mathematics and Information Science Weifang UniversityWeifangShandong 261061China

In this paper,we consider the exterior Dirichlet problem of Hessian equationsσk(λ(D^(2)u))=g(x)with g being a perturbation of a general positive function at *** existence of the viscosity solutions with generalized asymptotic behavior at infinity is established by the Perron’s method which extends the previous results for Hessian *** the solutions of Bernoulli ordinary differential equations,the viscosity subsolutions and supersolutions are constructed.

关键词： Hessian equations exterior Dirichlet problem asymptotic behavior

Complicated asymptotic behavior of Solutions for the Cauchy Problem of Doubly Nonlinear Diffusion Equation

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Communications in Mathematical Research 2023年第2期39卷 231-253页

作者： Liang-Wei Wang Shu-Ying Wang Jingxue Yin Zheng-Wen Tu College of Mathematics and Statistics Chongqing Three Gorges UniversityChongqing 404100China School of Mathematical Science South China Normal UniversityGuangzhou 510631China

In this paper,we analyze the large time behavior of nonnegative solutions to the doubly nonlinear diffusion equation u_(t)−div(|∇u^(m)|^(p−2)∇u^(m))=0 in R^(N)with p>1,m>0 and m(p−1)−1>*** using the finite propagation property and the L^(1)−L^(∞)smoothing effect,we find that the complicated asymptotic behavior of the rescaled solutions t^(μ/2)u(t^(β)⋅,t)for 0(2−μ[m(p−1)−1])/(2 p)can take place.

关键词： Complexity asymptotic behavior doubly nonlinear diffusion equation

asymptotic behavior of Global Solution for Nonlinear Generalized Euler-Possion-Darboux Equation

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Chinese Quarterly Journal of Mathematics 2004年第3期19卷 247-252页

作者： LIANGBao-song CHENZhen BasicScienceCollege HenanAgriculturalUniversityZhengzhou450002China

J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate... 详细信息

关键词： nonlinear generalized Euler-Possion-Darboux equation difference inequality global solution asymptotic behavior

On the asymptotic behavior of Certain Second Order Differential Equations

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Chinese Quarterly Journal of Mathematics 2004年第2期19卷 186-187页

作者： XUZhi-ting XIAYong DepartmentofMathematics SouthChinaNormalUniversityGuangzhou510631China DepartmeritofMathematics DongguanInstituteofTechnologyDongguan511700China

Two criteria for asymptotic behavior of certain second order differential equations are obtained. The results extend and improve Feng's theorem.

关键词： asymptotic behavior second order differential equation bounded

asymptotic behavior of Solutions for a Class of Retarded Difference Equations

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Acta Mathematica Sinica,English Series 1998年第3期14卷 419-422页

作者： Huang Lihong Yu Jianshe Dai Binxiang Department of Applied Mathematics, Hunan University, Changsha 410082, China Department of Applied Mathematics Hunan University 410082 Changsha China

Consider the retarded difference equation xn-xn-1=F（-f（xn）+g（xn-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）>0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.

关键词： Retarded difference equation asymptotic behavior

asymptotic behavior of Oscillatory Solutions of Forced Nonlinear Neutral Delay Differential Equations

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Chinese Quarterly Journal of Mathematics 1998年第2期13卷 31-35,页

作者：罗交晚侯振挺贺春田 Department

The aim of this paper is to study the asymptotic behavior of the oscillatory solutions of forced nonlinear neutral equations of the form[x(t)-∑mi=1p i(t)x(t-τ i)]′+∑nj=1q j(t)f(x(t-σ j))=r(t),t≥t 0,where p i,q j,r∈C([t 0,∞),R),τ i,σ j≥0,i=1,2,…,m,j=1,2,…,n,f∈C(R,R),xf(x)>0 for x≠0. The results obtained here extend and improve some of the results of Ladas and Sficas [3] and *** [5].

关键词： oscillatory solution nonlinear neutral equations forced term asymptotic behavior

Global Existence, asymptotic behavior and Uniform Attractors for Damped Timoshenko Systems

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Chinese Quarterly Journal of Mathematics 2017年第3期32卷 305-321页

作者： HU Wen-song QIN Yu-ming College of Science Donghua University Shanghai 201620 China Departraent of Applied Mathe- matics Donghua University Shanghai 201620 China

In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets.

关键词： Timoshenko systems global existence semigroup methods asymptotic behavior uniform attractors

asymptotic behavior of a Bi-Dimensional Hybrid System

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Applied Mathematics 2015年第8期6卷 1228-1234页

作者： Pedro Gamboa Jaime E.Munoz Octavio Vera Margareth Alves Departamento de Matemática Instituto de MatemáticasUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil Laboratorio Nacional de Computacao Científica PetrópolisBrazil Departamento de Matemática Facultad de CienciasUniversidad del Bo-BoConcepciónChile Departamento de Matemática UFVVicosaBrazil

We study the asymptotic behavior of the solutions of a Hybrid System wrapping an elliptic operator.

关键词： Hybrid System Compressible Stabilization asymptotic behavior Decay Rate Generator Infinitesimal Polynomial Decay

asymptotic behavior OF SOLUTIONS TO A CLASS OF HIGHER ORDER NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

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Annals of Differential Equations 2009年第2期25卷 208-218页

作者： Jianli Yao (Science School,Shandong Jianzhu University,Ji’nan 250101) Ping Kang (Dept. of Math.,Tianjin Polytechnic University,Tianjin 300160) Fanwei Meng (Dept. of Math.,Qufu Normal University,Qufu 273165,Shandong) Science School Shandong Jianzhu University Ji'nan 250101 Dept. Of Math. Tianjin Polytechnic University Tianjin 300160 Dept. Of Math. Qufu Normal University Qufu P73165 Shandong

In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our... 详细信息

关键词： asymptotic behavior higher order integro-differential equations deviating arguments integro-inequality