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SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION
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作者 向长林 郑高峰 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期420-430,共11页
This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽... This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems. 展开更多
关键词 fourth order elliptic equation regularity theory Morrey space decay estimates Riesz potential
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MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE 被引量:3
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作者 许丽萍 陈海波 《Acta Mathematica Scientia》 SCIE CSCD 2015年第5期1067-1076,共10页
In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-(a+bfR^3|↓△u|^2dx)△u+V(x)u=f(x,u),x∈R^3, u∈H^2(R3),where a, b 〉 0 are constants and the primitive... In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-(a+bfR^3|↓△u|^2dx)△u+V(x)u=f(x,u),x∈R^3, u∈H^2(R3),where a, b 〉 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti- Rabinowitz type condition. 展开更多
关键词 fourth order elliptic equations of Kirchhoff type symmetric mountain pass theorem variational methods
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ON STABILITY OF SOLUTIONS OF CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS 被引量:5
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作者 Cemil Tunc 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第8期1141-1148,共8页
By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established re... By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature. 展开更多
关键词 non-linear delay differential equations of fourth order STABILITY Liapunov functional approach
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The Energy-orthogonal Tetrahedral Finite Element for Fourth Order Elliptic Equations 被引量:1
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作者 LIU Ming-fang CAO Ji-wei CHEN Shao-chun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期388-393,共6页
In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three... In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions.The newly constructed element is proved to be convergent for a model biharmonic equation. 展开更多
关键词 nonconforming finite element tree-dimension fourth order elliptic equation
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ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD 被引量:1
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作者 Cemil TUNC Aydin TIRYAKI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第11期1039-1049,共11页
In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the sol... In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results. 展开更多
关键词 nonlinear differential equations of the fourth order Lyapunovfunction STABILITY BOUNDEDNESS intrinsic method
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Asymptotic behaviour of solution for fourth order wave equation with dispersive and dissipative terms
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作者 徐润章 赵希人 沈继红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第2期259-262,共4页
This paper studies the initial boundary value problem of fourth order wave equation with dispersive and dissipative terms. By using multiplier method, it is proven that the global strong solution of the problem decays... This paper studies the initial boundary value problem of fourth order wave equation with dispersive and dissipative terms. By using multiplier method, it is proven that the global strong solution of the problem decays to zero exponentially as the time approaches infinite, under a very simple and mild assumption regarding the nonlinear term. 展开更多
关键词 fourth order wave equation DISPERSIVE DISSIPATIVE asymptotic behaviour
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BLOWING UP AND MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER EQUATION WITH CRITICAL NONLINEARITY
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作者 Siwar AMMAR Mokhles HAMMAMI 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1511-1546,共36页
In this paper, we consider the following nonlinear elliptic problem : △2u =|u|n-4^-u+u|u|q-1u,in Ω,△u=u=0 on ЭΩ,where Ω is a bounded and smooth domain in R^n,n∈{5,6,7},u is a parameter and q∈]4/(n-4)... In this paper, we consider the following nonlinear elliptic problem : △2u =|u|n-4^-u+u|u|q-1u,in Ω,△u=u=0 on ЭΩ,where Ω is a bounded and smooth domain in R^n,n∈{5,6,7},u is a parameter and q∈]4/(n-4),(12-n)/(n-4)].We study the solutions which concentrate around two points of Ω. We prove that the concentration speeOs are the same order and the distances of the concentration points from each other and from the boundary are bounded. For Ω=(Ωa)a a smooth ringshaped open set, we establish the existence of positive solutions which concentrate at two points of Ω. Finally, we show that for u〉0, large enough, the problem has at least many positive solutions as the Ljusternik-Schnirelman category of Ω. 展开更多
关键词 fourth order elliptic equations critical Sobolev exponent blow up solution
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On the Oscillation of the Fourth Order Differential Equations
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作者 冯滨鲁 俞元洪 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第4期1-10, ,共10页
In the present paper sufficient conditions for oscillations and nonoscillations of a class of fourth order differential equations are obtained.
关键词 fourth order differential equations oscillatory solutions nonoscillatory solutions
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BOUNDEDNESS AND UNIFORM BOUNDEDNESS RESULTS FOR CERTAIN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF FOURTH ORDER
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作者 Cemil Tunc(西密尔·通兹) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第11期1273-1278,共6页
Sufficient conditions have been obtained so that all solutions of a different fourth order differential equation are bounded and uniformly bounded.
关键词 differential equation of fourth order Liapunov function BOUNDEDNESS uniform boundedness
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Solvability of 4-Point Boundary Value Problems at Resonance for Fourth-Order Ordinary Differential Equations
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作者 张祖峰 魏章志 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第4期935-944,共10页
In this paper, we consider the following fourth order ordinary differential equation x(4)(t) = f(t,x(t),x (t),x (t),x (t)), t ∈ (0,1) (E) with the four-point boundary value conditions: x(0) = x(1) = 0, αx (ξ1) - β... In this paper, we consider the following fourth order ordinary differential equation x(4)(t) = f(t,x(t),x (t),x (t),x (t)), t ∈ (0,1) (E) with the four-point boundary value conditions: x(0) = x(1) = 0, αx (ξ1) - βx (ξ1) = 0, γx (ξ2) + δx (ξ2) = 0, (B) where 0 < ξ1 < ξ2 < 1. At the resonance condition αδ + βγ + αγ(ξ2 - ξ1) = 0, an existence result is given by using the coincidence degree theory. We also give an example to demonstrate the result. 展开更多
关键词 fourth order equation RESONANCE coincidence degree.
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Exact Controllability for the Fourth Order Schrdinger Equation 被引量:1
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作者 Chuang ZHENG Zhongcheng ZHOU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第3期395-404,共10页
The boundary controllability of the fourth order Schr5dinger equation in a bounded domain is studied. By means of an L2-Neumann boundary control, the authors prove that the solution is exactly controllable in H-2(12... The boundary controllability of the fourth order Schr5dinger equation in a bounded domain is studied. By means of an L2-Neumann boundary control, the authors prove that the solution is exactly controllable in H-2(12) for an arbitrarily small time. The method of proof combines both the HUM (Hilbert Uniqueness Method) and multiplier techniques. 展开更多
关键词 fourth order Schroedinger equation HUM method CONTROLLABILITY MULTIPLIER
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STABILITY OF SOLUTIONS TO CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS 被引量:2
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作者 Huiyan Kang (School of Math. and Physics, Changzhou University, Changzhou 213016, Jiangsu) Ligeng Si (Dept. of Math., Inner Mongolia Normal University, Huhhot 010020) 《Annals of Differential Equations》 2010年第4期407-413,共7页
By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to ... By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained. 展开更多
关键词 non-linear delay differential equation of fourth order stability Lyapunov functions
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Strong unique continuation property for a class of fourth order elliptic equations with strongly singular potentials
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作者 Hairong Liu Xiaoping Yang 《Science China Mathematics》 SCIE CSCD 2022年第4期707-730,共24页
In this paper we prove the strong unique continuation property for a class of fourth order elliptic equations involving strongly singular potentials.Our argument is to establish some Hardy-Rellich type inequalities wi... In this paper we prove the strong unique continuation property for a class of fourth order elliptic equations involving strongly singular potentials.Our argument is to establish some Hardy-Rellich type inequalities with boundary terms and introduce an Almgren’s type frequency function to show some doubling conditions for the solutions to the above-mentioned equations. 展开更多
关键词 strong unique continuation property fourth order elliptic equation singular potential Hardy-Rellich type inequality
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Null controllability for a fourth order parabolic equation
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作者 YU Hang 《Science in China(Series F)》 2009年第11期2127-2132,共6页
In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of ... In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of eigenfunctions of the Laplacian. 展开更多
关键词 fourth order parabolic equations null controllability Lebeau-Rabbiano inequality
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One-Dimensional Symmetry and Liouville Type Results for the Fourth Order Allen-Cahn Equation in R^N
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作者 Denis BONHEURE Franois HAMEL 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2017年第1期149-172,共24页
In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at in... In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities. 展开更多
关键词 fourth order elliptic equation Allen-Cahn equation Extended Fisher-Kolmogorov equation One-dimensional symmetry Liouville type results
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ON THE EXISTENCE OF PERIODIC SOLUTIONS TO A CERTAIN FOURTH-ORDER NONLINEAR DIFFERENTIAL EQUATION
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作者 Cemil Tun 《Annals of Differential Equations》 2009年第1期8-12,共5页
In this paper, we consider a certain fourth-order nonlinear ordinary differential equation. Some sufficient conditions which guarantee the existence of at least one ω-periodic solution to the system are obtain.
关键词 nonlinear differential equations of fourth order existence of periodic solutions
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ON THE ULTIMATE BOUNDEDNESS RESULT FOR THE SOLUTIONS OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS
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作者 CemilTunc 《Annals of Differential Equations》 1998年第3期475-485,共11页
The main purpose of this paper is to give sufficient conditions, which ensurethat all solutions of (1 .1) are ultimately bounded.
关键词 non-linear differential equations of the fourth order boundedness
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STABILITY AND CONVERGENCE ANALYSIS OF SECOND-ORDER SCHEMES FOR A DIFFUSE INTERFACE MODEL WITH PENG-ROBINSON EQUATION OF STATE 被引量:1
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作者 Qiujin Peng Zhonghua Qiao Shuyu Sun 《Journal of Computational Mathematics》 SCIE CSCD 2017年第6期737-765,共29页
In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mas... In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes. 展开更多
关键词 Diffuse interface model fourth order parabolic equation Energy stability Convergence.
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JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS 被引量:1
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作者 Zheng-su Wan Ben-yu Guo Zhong-qing Wang 《Journal of Computational Mathematics》 SCIE EI CSCD 2006年第4期481-500,共20页
In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as im... In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis. 展开更多
关键词 Jacobi pseudospectral method Differential equations of fourth order Singular problems.
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STRESS EFFECT DECAY ESTIMATES FOR ANISOTROPIC MATERIAL IN A SEMI-INFINITE STRIP
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作者 蔡崇喜 林长好 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第3期300-308,共9页
In this paper, Saint-Venant's principle for anisotropic material in an end-loaded. semi-infinite elastic strip is established. Energy method is used to establish the lower bounds of the decay estimate of stress ef... In this paper, Saint-Venant's principle for anisotropic material in an end-loaded. semi-infinite elastic strip is established. Energy method is used to establish the lower bounds of the decay estimate of stress effect. An explicit estimate formula in terms of the elastic constants of the anisotropic materials is presented. Finally, a numerical example for an end-loaded, off-axis, graphite-epoxy strip is given to illustrate the results. 展开更多
关键词 Saint-Venant's principle fourth order elliptic equation energy method material anisotropy stress decay estimate
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