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Remarks on Oscillation for Systems of High Order Partial Differential Equations of Neutral Type
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作者 LIN Wen-xian 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期537-542,共6页
In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
关键词 neutral type system of partial differential equations oscillation
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FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS
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作者 靳明忠 董莹 李崇孝 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第9期889-900,共12页
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish... In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities. 展开更多
关键词 higher order functional partial differential equation boundary value problems forced oscillation
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Oscillation for Solutions of Systems of High Order Partial Differential Equations of Neutral Type 被引量:8
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作者 LIN Wen-xian(Department of Mathematics, Hanshan Teacher’s College, Chaozhou 521041, China) 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第2期168-174,共7页
In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
关键词 neutral type system of partial differential equations oscillation
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Oscillation of Nonlinear Impulsive Delay Hyperbolic Partial Differential Equations 被引量:2
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作者 罗李平 彭白玉 欧阳自根 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第3期439-444,共6页
In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differen... In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained. 展开更多
关键词 NONLINEAR IMPULSE DELAY hyperbolic partial differential equations oscillation
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NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF NEUTRAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAYS 被引量:2
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作者 Yang Jun Wang Ghunyan Li Jing Meng Zhijuan 《Journal of Partial Differential Equations》 2006年第4期319-324,共6页
This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations,... This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples. 展开更多
关键词 partial differential equation neutral hyperbolic type delay oscillation.
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Oscillation of Solutions for a Class of Nonlinear Neutral Partial Differential Equations with Continuous Distribution Delay
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作者 罗李平 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第1期67-74,共8页
In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and D... In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet's boundary value conditions. 展开更多
关键词 NONLINEAR NEUTRAL partial differential equation oscillation continuous distribution delay
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The advancement of oscillation theory of functional differential equations 被引量:1
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作者 ZHANG Binggen Department of Applied Mathematics, Ocean University of Qingdao, Qingdao 266003, China 《Chinese Science Bulletin》 SCIE EI CAS 1998年第12期974-982,共9页
The oscillation theory of functional differential equations (FDEs) is surveyed including (ⅰ) formulation of oscillation problems; (ⅱ) a brief history of the oscillation theory of FDEs; (ⅲ) main topics in the oscill... The oscillation theory of functional differential equations (FDEs) is surveyed including (ⅰ) formulation of oscillation problems; (ⅱ) a brief history of the oscillation theory of FDEs; (ⅲ) main topics in the oscillation theory of FDEs; (ⅳ) open problems in the oscillation theory of FDEs. 展开更多
关键词 functional differential equations oscillation theory.
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FORCED OSCILLATION AND APPLICATION OF FUNCTIONAL DIFFERENTIAL INEQUALITIES
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作者 靳明忠 董莹 李崇孝 《Annals of Differential Equations》 2002年第3期217-225,共9页
In this paper we study the oscillations for a class of functional differential inequalities. By using these properties some forced oscillations to the boundary value problems of functional partial differential equatio... In this paper we study the oscillations for a class of functional differential inequalities. By using these properties some forced oscillations to the boundary value problems of functional partial differential equations are established. 展开更多
关键词 functional differential inequality partial differential equations forced oscillation
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On the partial stability of nonlinear impulsive Caputo fractional systems
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作者 Boulbaba Ghanmi Saifeddine Ghnimi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期166-179,共14页
In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated.Some effective sufficient conditions of stability,uniform stability,asymptot... In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated.Some effective sufficient conditions of stability,uniform stability,asymptotic uniform stability and Mittag Leffler stability.The approach presented is based on the specially introduced piecewise continuous Lyapunov functions.Furthermore,some numerical examples are given to show the effectiveness of our obtained theoretical results. 展开更多
关键词 impulsive fractional differential equations Mittag-Leffler function partial stability Caputo derivative
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Periodic Solutions in UMD Spaces for Some Neutral Partial Functional Differential Equations 被引量:1
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作者 Rachid Bahloul Khalil Ezzinbi Omar Sidki 《Advances in Pure Mathematics》 2016年第10期713-726,共15页
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s... The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces. 展开更多
关键词 Neutral partial functional differential equations Periodic Solutions R-BOUNDEDNESS Lp-Multipliers UMD Spaces
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New Kamenev-type Oscillation Criteria for Half-linear Partial Differential Equations
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作者 Ge-feng YANG Zhi-ting XU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2012年第3期535-548,共14页
We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div(A(x)|| u||^p-2 u)+〈b(x),|| u||^p-2 u〉+c(x)|u|^p-2u=0(E)under quite general ... We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div(A(x)|| u||^p-2 u)+〈b(x),|| u||^p-2 u〉+c(x)|u|^p-2u=0(E)under quite general conditions. These results are extensions of the recent results developed by Sun [Y.C. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations. 展开更多
关键词 oscillation HALF-LINEAR partial differential equations Kamenev-type Damped equation
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Oscillation Criteria for Even Order Functional Differential Equations with Damped Term
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作者 Ailing Shi 《数学计算(中英文版)》 2015年第4期77-82,共6页
This paper investigates a class of even order functional differential equations with damped term,and derives two new oscillatory criteria of solution.
关键词 functional differential EQUATION EVEN Order DAMPED oscillation
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A problem of complex oscillation for homogeneous linear differential equations 被引量:2
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作者 GAO Shian and YANG Ronghua Department of Mathematics,South China Normal University,Guangzhou 510631, China Department of Mathematics, Guangdong Educational College, Guangzhou 510303, China 《Chinese Science Bulletin》 SCIE EI CAS 1998年第20期1709-1712,共4页
Under a combined dominant condition, an open problem of complex oscillation for the equation \%w (k) +Aw=0\% is set, where \%k≥3, a(z)\% is a transcendental entire function.
关键词 MEROMORPHIC function differential EQUATION complex oscillation.
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Oscillation for a Class of Fractional Differential Equation 被引量:2
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作者 Qian Feng Anping Liu 《Journal of Applied Mathematics and Physics》 2019年第7期1429-1439,共11页
We consider the oscillation of a class fractional differential equation with Robin and Dirichlet boundary conditions. By generalized Riccati transformation technique and the differential inequality method, oscillation... We consider the oscillation of a class fractional differential equation with Robin and Dirichlet boundary conditions. By generalized Riccati transformation technique and the differential inequality method, oscillation criteria for a class of nonlinear fractional differential equation are obtained. 展开更多
关键词 oscillation FRACTIONAL DERIVATIVE FRACTIONAL partial differential EQUATION
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OSCILLATION FOR SOLUTIONS OF SYSTEMS OF N-TH ORDER PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS 被引量:6
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作者 林文贤 《Annals of Differential Equations》 2004年第3期266-272,共7页
In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.
关键词 system of partial functional differential equations oscillation
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OSCILLATORY BEHAVIOR FOR HIGH ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS
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作者 林文贤 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第8期789-800,共12页
In this paper, the oscillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure. It is found that the nonoscillatory solutions only have two kinds on som... In this paper, the oscillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure. It is found that the nonoscillatory solutions only have two kinds on some conditions. And necessary conditions for the existence of each kind of nonoscillatory solutions are presented as well. At the same ime, some sufficient conditions for oscillatory solutions are also established. 展开更多
关键词 functional differential equation oscillation NONLINEAR Lebesgue measure
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A Comparative Numerical Study of Parabolic Partial Integro-Differential Equation Arising from Convection-Diffusion
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作者 Kamil Khan Arshed Ali +2 位作者 Fazal-i-Haq Iltaf Hussain Nudrat Amir 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第2期673-692,共20页
This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation(PIDE)with a weakly singular kernel.Cubic trigonometric B-spline(CTBS)functio... This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation(PIDE)with a weakly singular kernel.Cubic trigonometric B-spline(CTBS)functions are used for interpolation in both methods.The first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear equations.The other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function values.An efficient tridiagonal solver is used for the solution of the linear system obtained in the first method as well as for determination of weighting coefficients in the second method.An explicit scheme is employed as time integrator to solve the system of ODEs obtained in the second method.The methods are tested with three nonhomogeneous problems for their validation.Stability,computational efficiency and numerical convergence of the methods are analyzed.Comparison of errors in approximations produced by the present methods versus different values of discretization parameters and convection-diffusion coefficients are made.Convection and diffusion dominant cases are discussed in terms of Peclet number.The results are also compared with cubic B-spline collocation method. 展开更多
关键词 partial integro-differential equation CONVECTION-DIFFUSION collocation method differential quadrature cubic trigonometric B-spline functions weakly singular kernel
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Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations
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作者 LIU Shi-Da FU Zun-Tao LIU Shi-Kuo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第3X期425-427,共3页
In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.
关键词 Jacobi elliptic function periodic wave solution nonlinear partial differential equation
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The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation
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作者 Daniel A. Jaffa 《Journal of Applied Mathematics and Physics》 2024年第1期98-125,共28页
Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of ... Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation. 展开更多
关键词 Hessian Matrices Jacobian Matrices Laplace Equation Linear partial differential equations systems of partial differential equations Harmonic Functions Incompressible and Irrotational Fluid Mechanics
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Influence of Waveguide Properties on Wave Prototypes Likely to Accompany the Dynamics of Four-Wave Mixing in Optical Fibers
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作者 Jean Roger Bogning Marcelle Nina Zambo Abou’ou +4 位作者 Christian Regis Ngouo Tchinda Mathurin Fomekong Oriel Loh Ndichia Stallone Mezezem Songna François Béceau Pelap 《Journal of Applied Mathematics and Physics》 2024年第7期2601-2633,共33页
In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of... In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest. 展开更多
关键词 Optical Fiber Four Waves Mixing Implicit Bogning Function Coupled Nonlinear partial differential equations Nonlinear Coefficient Dispersive Coefficient Waveguide Properties
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