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Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term
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作者 李想 张卫国 +1 位作者 李正明 Ji-bin LI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第1期117-132,共16页
This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of pla... This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form. 展开更多
关键词 nonlinear wave equation bounded traveling wave solution shape analysis approximate damped oscillatory solution error estimate
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Asymptotic Behavior of Oscillatory Solutions of Forced Nonlinear Neutral Delay Differential Equations
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作者 罗交晚 侯振挺 贺春田 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第2期31-35, ,共5页
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 ... 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 J.R.Yan [5]. 展开更多
关键词 oscillatory solution nonlinear neutral equations forced term asymptotic behavior
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EXISTENCE OF OSCILLATORY SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH "MAXIMA
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作者 张炳根 《Annals of Differential Equations》 2000年第2期177-183,共7页
In this paper, sufficient conditions for the existence of oscillatory solutions of neutral differential equations with 'maxima' are obtained.
关键词 oscillatory solutions neutral differential equations MAXIMA
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Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prufer transformation
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作者 LI Zhi-yu LI Kun +2 位作者 CAI Jin-ming QIN Jian-fang ZHENG Zhao-wen 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期191-200,共10页
A class of Sturm-Liouville problems with discontinuity is studied in this paper.The oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are obtained.The main method used in ... A class of Sturm-Liouville problems with discontinuity is studied in this paper.The oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are obtained.The main method used in this paper is based on Prufer transformation,which is different from the classical ones.Moreover,we give two examples to verify our main results. 展开更多
关键词 Sturm-Liouville problem interface condition oscillatory solution
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Quadratic integrability of solutions based on a class of delayed systems
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作者 计国君 《Journal of Southeast University(English Edition)》 EI CAS 2007年第4期630-638,共9页
Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function,... Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice. 展开更多
关键词 nonlinear delayed system quadratic integrability periodic solution oscillatory solution OVERVOLTAGE
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OSCILLATORY BEHAVIOUR OF A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS OF THIRD ORDER 被引量:10
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作者 A. Tiryaki Department of Mathematics, Gazi University Faculty of Arts and Sciences Teknik Okullar, 06500 Ankara, Turkey S. (Yaman) Pasinlio■u Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkey 《Acta Mathematica Scientia》 SCIE CSCD 2001年第2期182-188,共7页
This paper investigates the oscillatory and nonoscillatory behaviour of solu- tions of a class of third order nonlinear differential equations. Results extend and improve some known results in the literature.
关键词 oscillatory solution nonoscillatory solution behaviour of solution nonlinear differential equation
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OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF NONLINEAR DIFFERENTIALEQUATIONS OF THIRD ORDER 被引量:2
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作者 N. Parhi P. Das(Department of Mathematics, Berhampur University, Bechampur-760007, India) 《Acta Mathematica Scientia》 SCIE CSCD 1998年第1期95-106,共12页
This paper deals with oscillatory /nonoscillatory behaviour of solutions of thirdorder nonlinear differential equations of the formwhere a,b,c E C([a,oo),R) such that a(t) does not change sign, b(t) 5 0, c(t) > 0,f... This paper deals with oscillatory /nonoscillatory behaviour of solutions of thirdorder nonlinear differential equations of the formwhere a,b,c E C([a,oo),R) such that a(t) does not change sign, b(t) 5 0, c(t) > 0,f∈C(R, R) such that (f(y)/y) ≥ β > 0 for y ≠ 0 and γ > 0 is a quotient of odd integers.It has been shown, under certain conditions on coefficient functions, that a solution of (1)and (2) which Las a zero is oscillatory and the nonoscillatory solutions of these equationstend to zero as t → ∞. The motivation for this work came from the observation that thewhere al b, c are constants such that b≤ 0, c > 0, has an oscillatory solution if and only ifand all nonoscillatory solutions of (3) tend to zero if and only if the equation has anoscillatory solution. 展开更多
关键词 oscillatory solution nonoscillatory solution behaviour of solution nonlinear differential equation
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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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New Oscillation Criteria for Second Order Half-Linear Neutral Type Dynamic Equations on Time Scales 被引量:1
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作者 Faisal Al-Dheleai Elmetwally Elabbasy 《Journal of Applied Mathematics and Physics》 2021年第9期2376-2398,共23页
In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscill... In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscillation of all solutions of this equation. Our results not only unify the oscillation of second order nonlinear differential and difference equations but also can be applied to different types of time scales with sup T = ∞. Our results improve and extend some known results in the literature. Examples which dwell upon the importance of our results are also included. 展开更多
关键词 Dynamic Equation oscillatory solutions NEUTRAL Deviating Arguments
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SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS
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作者 E.M.E.Zayed M.A.El-Moneam 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期602-610,共9页
The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations(a(t)x'(t))'+δ1p(t)x'(t) +δ2q(t)f(x(g(t))) ... The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations(a(t)x'(t))'+δ1p(t)x'(t) +δ2q(t)f(x(g(t))) = 0,for 0 ≤ to≤ t, where 51 = :El and δ±1. The functions p,q,g : [t0, ∞) → R, f : R → are continuous, a(t) 〉 0,p(t) ≥0,q(t) 〉 0 for t ≥ to,lirn g(t) = ∞, and q is not identically zero on any subinterval of [to, ∞). Moreover, the functions q(t), g(t), and a(t) are continuously differentiable. 展开更多
关键词 oscillatory and nonoscillatory solutions nonlinear functional differential equations
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Oscillatory Periodic Solutions of Nonlinear Second Order Ordinary Differential Equations 被引量:1
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作者 Yong Xiang LI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第3期491-496,共6页
In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation -u″(t) = f(t, u(t)), where f : R^2 → R is a continuous odd function and is ... In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation -u″(t) = f(t, u(t)), where f : R^2 → R is a continuous odd function and is 2π-periodic in t. The discussion is based on the fixed point index theory in cones. 展开更多
关键词 Second order differential equation oscillatory periodic solution CONE Fixed point index
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On the contact width in generalized plain strain JKR model for isotropic solids
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作者 Cong Yan Shaohua Chen LNM, Institute of Mechanics, Chinese Academy of Sciences,100190 Beijing. China 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第4期491-497,共7页
Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the conta... Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs' parameter 13 or the larger the pulling angle O, the more reasonable the symmetric model would be to approximate the asymmetric one. 展开更多
关键词 Contact mechanics Generalized JKRmodel Asymmetric contact width oscillatory solution Non-oscillatory solution
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Shape Analysis of Bounded Traveling Wave Solutions and Solution to the Generalized Whitham-Broer-Kaup Equation with Dissipation Terms
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作者 Weiguo ZHANG Qiang LIU +1 位作者 Xiang LI Boling GUO 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第2期281-308,共28页
This paper deals with the problem of the bounded traveling wave solutions' shape and the solution to the generalized Whitham-Broer-Kaup equation with the dissipation terms which can be called WBK equation for shor... This paper deals with the problem of the bounded traveling wave solutions' shape and the solution to the generalized Whitham-Broer-Kaup equation with the dissipation terms which can be called WBK equation for short.The authors employ the theory and method of planar dynamical systems to make comprehensive qualitative analyses to the above equation satisfied by the horizontal velocity component u(ξ) in the traveling wave solution (u(ξ),H(ξ)),and then give its global phase portraits.The authors obtain the existent conditions and the number of the solutions by using the relations between the components u(ξ) and H(ξ) in the solutions.The authors study the dissipation effect on the solutions,find out a critical value r*,and prove that the traveling wave solution (u(ξ),H(ξ)) appears as a kink profile solitary wave if the dissipation effect is greater,i.e.,|r| ≥ r*,while it appears as a damped oscillatory wave if the dissipation effect is smaller,i.e.,|r| < r*.Two solitary wave solutions to the WBK equation without dissipation effect is also obtained.Based on the above discussion and according to the evolution relations of orbits corresponding to the component u(ξ) in the global phase portraits,the authors obtain all approximate damped oscillatory solutions (u(ξ),H(ξ)) under various conditions by using the undetermined coefficients method.Finally,the error between the approximate damped oscillatory solution and the exact solution is an infinitesimal decreasing exponentially. 展开更多
关键词 Generalized Whitham-Broer-Kaup equation Shape analysis Solitarywave solution Damped oscillatory solution Error estimate
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Qualitative Analysis and Solutions of Bounded Traveling Wave for B-BBM Equation
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作者 Yan Zhao Wei-guo Zhang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2010年第3期415-426,共12页
In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter cond... In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coeffiicient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented. 展开更多
关键词 B-BBM equation qualitative analysis global phase portrait solitary wave solution damped oscillatory solution
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Oscillatory solution to semilinear dissipative wave equations
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《Chinese Science Bulletin》 SCIE CAS 1998年第9期787-788,共2页
关键词 WAVE MATH oscillatory solution to semilinear dissipative wave equations
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Shape Analysis and Solution to a Class of NonlinearWave Equation with Cubic Term
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作者 Xiang Li Weiguo Zhang Yan Zhao 《Advances in Applied Mathematics and Mechanics》 SCIE 2012年第5期559-574,共16页
In this paper,we analyze the relation between the shape of the bounded traveling wave solutions and dissipation coefficient of nonlinear wave equation with cubic term by the theory and method of planar dynamical syste... In this paper,we analyze the relation between the shape of the bounded traveling wave solutions and dissipation coefficient of nonlinear wave equation with cubic term by the theory and method of planar dynamical systems.Two critical values which can characterize the scale of dissipation effect are obtained.If dissipation effect is not less than a certain critical value,the traveling wave solutions appear as kink profile;while if it is less than this critical value,they appear as damped oscillatory.All expressions of bounded traveling wave solutions are presented,including exact expressions of bell and kink profile solitary wave solutions,as well as approximate expressions of damped oscillatory solutions.For approximate damped oscillatory solution,using homogenization principle,we give its error estimate by establishing the integral equation which reflects the relations between the exact and approximate solutions.It can be seen that the error is an infinitesimal decreasing in the exponential form. 展开更多
关键词 Nonlinear wave equation planar dynamical system exact solutions approximate damped oscillatory solutions error estimate
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