Periodic Solutions for a Class of Forced Lienard-type Equations

By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Lienard-type equation Our results extend and improve some known results in the literature.     

Existence of Periodic Solutions for a Class of Nonlinear Ordinary Differential Equations of Higher Order

ＥｘｉｓｔｅｎｃｅｏｆＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｆｏｒａＣｌａｓｓｏｆＮｏｎｌｉｎｅａｒＯｒｄｉｎａｒｙＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓｏｆＨｉｇｈｅｒＯｒｄｅｒＬｉｕＺｈａｏｌｉ（刘兆理）（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｓｈａｎｄｏｎ...     

Homoclinic Solutions for a Forced Liénard Type System

In this paper, we find a special class of homoclinic solutions which tend to 0 as t → ±∞, for a Liénard type system with a time-dependent force. Since it is not a small perturbation of a Hamiltonian system, we cannot employ the well-known Melnikov method to determine the existence of homoclinic solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. We prove that the sequence of those periodic solutions has an accumulation which gives an homoclinic solution of the forced Liénard type system.     

Local Bifurcation of Critical Periods for a Class of Liénard Equations

In this paper,we study the local bifurcation of critical periods near the nondegenerate center(the origin) of a class of Liénard equations with degree 2n,and prove that at most 2n-2 critical periods(taken into account multiplicity) can be produced from a weak center of finite order.We also prove that it can have exactly2n-2 critical periods near the origin.     

Stability of Solutions for a Class of Quasilinear Degenerate Parabolic Equations

ＳｔａｂｉｌｉｔｙｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＣｌａｓｓｏｆＱｕａｓｉｌｉｎｅａｒＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎｓ￥ＺｈａｏＪｕｎｎｉｎｇ（赵俊宁）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔ...     

Existence of Positive Periodic Solutions for the Liénard Differential Equations with Weakly Repulsive Singularity

In this paper we discuss the existence of positive T-periodic solutions for the following second order differential equation

Periodic Solutions for Nonlinear Diferential Equations

ＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｆｏｒＮｏｎｌｉｎｅａｒＤｉｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓＣｏｎｇＦｕｚｈｏｎｇ（从福仲）（ＯｆｆｉｃｅｏｆＭａｔｈｅｍａｔｉｃｓ，８６００３Ｕｎｉｔ，Ｃｈａｎｇｃｈｕｎ，１３００２２）ＭａｏＤｏｎｇｍｉｎｇ（...     

On Periodic Solutions of a Class of Differential Equation with Periodic Coefficients

51.IntroductionandtheLemmas.Thefollowingequationy'=f(t,y)=A(t)y" B(t)y C(t)(m22,meN)(l.1)(WhereA(t),B(t)andC(t)areallcontinuousT-periodicfunctions,TXO)isencounteredinseveralappliedareas,sincethisequationplaysanimportantroleinthestudiesofnonlinearos-cillation,fluidmechanicsandthequalitativetheoryofordinarydifferentialequation.Whenm=2,(1.1)isthefamousRiccatiEqation.In1979,ProfessorQinYuanxunansweredthequestionthatunderwhatconditionsRiccatiEquationwithperiodiccoefficientshasthecontinu-ous…     

The Problem of Periodic Solutions for a Class of Dynamical Systems（Ⅰ

ＴｈｅＰｒｏｂｌｅｍｏｆＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｆｏｒａＣｌａｓｓｏｆＤｙｎａｍｉｃａｌＳｙｓｔｅｍｓ（Ⅰ）ＺｈａｎｇＺｈｉｐｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，４７５００...     

The Periodic Solutions of Partial Variables for An Class of Linear Periodic Systems

ＴｈｅＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｏｆＰａｒｔｉａｌＶａｒｉａｂｌｅｓｆｏｒＡｎＣｌａｓｓｏｆＬｉｎｅａｒＰｅｒｉｏｄｉｃＳｙｓｔｅｍｓ￥ＷａｎｇＨｕｔ；ＬｕＭｅｎｇｌｉｎ（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ）（ＺｈｅｎｇｚｈｏｕＬｉｇｈｔＩｎｄｕ...     

Solutions to a Class of Differential—fuctional Equations

ＳｏｌｕｔｉｏｎｓｔｏａＣｌａｓｓｏｆＤｉｆｆｅｒｅｎｔｉａｌ－ｆｕｃｔｉｏｎａｌ　ＥｑｕａｔｉｏｎｓＬｉＺｅｍｉｎ（李泽民）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａ...     

The Problem of Periodic Solutions for a Class of Dynamical System（Ⅱ）

51.IntroductionLetK:R"XR"-Rbeasmoothfunctionwithi)K(q,p)isevenandstrictlyconvexinP,VqeR"lii)K(q,6)=o,VqeR".Supl>oseV=R"-Rbeasmoothfunction,t:R"-R"'(,n<)l)beaSubmersiveoperator.WIlereR",R,.arendimensionalEducli(leanspace,qeR",PeR",C(q)=(C,(q),C,(q),-.'C.,(q)).DenoteH(q,p)=K(q,p) V(q).Throughoutthispaper,weletZ(=(q,p))=6betheequilibriumpointofthefollowingsystem-ForoperatorC,wedefinethespeedoperatorofCisWhere,CisconsideredCorr,rristl1e1>rojeclionoperatorfromR"XR,,toI{.,anddf(z)…     

The Asymptotic Property of Solutions to a Class of Integrodifferential Equations

The asymptotic property of solutions to a class of integrodifferential systems containing a small parameter singularly is studied.     

Anti-periodic solutions for a class of Liénard-type systems with continuously distributed delays

This paper considers the Liénard-type systems with continuously distributed delays. Some new sufficient conditions for the existence and exponential stability of the anti-periodic solutions are established.     

Almost Periodic Solutions of Linear Neutral Integrodifferential Equations

The main purpose of this paper is to investigate the existence of almost periodic solutions of the linear neutral integrodifferential equation where D(t),A(t)and C(t)are n×n matrices defined on(—∞,∞),f(t)is an n-vector almost periodic function.To study equation(1),we consider     

Existence of limit cycles for Liénard-type systems with p-Laplacian

The purpose of this paper is to give sufficient conditions under which an equivalent system to the equation has at least one stable limit cycle, where is the one-dimensional p-Laplacian. The main results are proved by means of phase plane analysis with the Poincaré-Bendixson theorem. Sufficient conditions are also given for the origin to be unstable and for all solutions to be bounded in the future. Jitsuro Sugie: Supported in part by Grant-in-Aid for Scientific Research 16540152     

Asymptotic Behavior of Solutions to a Class of Systems of Delay Differential Equations

The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→∞. Our results improve and extend some corresponding ones already known.