Existence of Periodic Solutions for Odd Order Ordinary Differential Equations via the Homotopy Method

This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which will be stated later.The periodicity problem has been one of main topics in the qualitative theory of ordinary     

Existence of Positive Solutions for the Nonhomogeneous Schrödinger-Poisson System with Strong Singularity

In this paper, a class of nonhomogeneous Schrödinger-Poisson systems withstrong singularity are considered. Combining with the variational method and Neharimethod, we obtain a positive solution for this system which improves the recent resultsin the literature.     

Periodic Solutions for a Class of Forced Liénard-type Equations

Abstract   By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Liénard-type equation

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

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Global Existence of Positive Solutions for Volterra Integral Equations

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The Existence of Positive Almost Periodic Type Solutions for Some Nonlinear Delay Integral Equations

This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators （Ma, Y.： On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41（2）, 211-220 （1999]]. Some known results are operators.     

Existence and Uniqueness of Solutions of Differential Equations Weakly Controlled by Rough Paths with an Arbitrary Positive Hölder Exponent

Differential Equations - A functional version of the theory of rough paths with an arbitrary Hölder exponent is developed. It is used to prove a theorem on the existence and uniqueness of a...     

Asymptotic Behavior of Solutions of Certain Delay Differential Equations with Periodic Coefficients

§1 Introduction In [1], we have discussed the asymptotic behavior and structure of solutions of the linear delay differential equation (1.1) (r>0 is a real constant), and have obtained the following result: If p(t)=const., or p(t)>0 and integral from n=t to t+r(p(s)ds≥1) , then any solution x(t) of (1.1) can be expressed as     

Periodic solutions of the retarded Liénard equation

Consider the equation

Existence of Periodic Solutions About One Class Differential Equation

We discuss the existence and the number of periodic solutions of differential equation dx/dt=A1(t)x A2(t)x^2 A3(t)x^3/α0(t） α1(t)x α2(t)x^2 (1)where Ai（t），αj(t)(i=1,2,3;j=0,1,2) are continuous periodic functions.The results of this paper ex-tend the work of paper[1].     

Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations

g1.IntroductionWeconsiderthefollowingfirstorderquasilinearhyperbolicequationswithinternaIdissipa-tlveterm:U, A(U)U. F(U)=o(1.1)whereUeR2isunknownvectorfunction,A(U)is2X2knownsmoothmatrix,F(U)is2X2knownsmoothvectorfunction.Itiswell-knownthatCauchyproblemoftheequations(l.1)hasbeenwidelystudied(Ll-6J),however,theequations(l.1)withperiedicinitialdatahasbeenhardlystudiedandonesfindthatitiscomplicatedforproblemwithperiodicinitialdata.Becausetheperiodicdis-turbanceLlirectlyinfluencesthebounde…     

Existence of Positive Periodic Solutions for Nonautonomous Predator-prey Systems with Discrete and Continuously Distributed Delays

By using the continuation theorem of coincidence degree theory,the sufficient conditions to guar-antee the existence of positive periodic solutions are established for nonautonomous predator-prey systems withdiscrete and continuously distributed delays.     

Multiple Periodic Solutions of Differential Delay Equations with 2k-1 Lags

In this paper, we study the periodic solutions to a type of differential delay equations with 2 k-1 lags. The 4 k-periodic solutions are obtained by using the variational method and the method of Kaplan-Yorke coupling system. This is a new type of differential delay equations compared with all the previous researches.And this paper provides a theoretical basis for the study of differential delay equations. An example is given to demonstrate our main results.     

Stability of Solutions of Stochastic Differential Equations Weakly Controlled by Rough Paths with Arbitrary Positive Hölder Exponent

Differential Equations - We prove theorems on the stability of solutions of one-dimensional stochastic differential equations controlled by rough paths with arbitrary positive Hölder exponent.     

On the Existence of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equation

By means of the continuation theorem of coincidence degree theory, some new results on the non-existence, existence and unique existence of periodic solutions for a kind of second order neutral functional differential equation are obtained.     

Approximations for Solutions of Lévy-Type Stochastic Differential Equations

Abstract

The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for Lévy-type stochastic differential equation. In particular, the article generalizes the results from [2 Gardoń , A. 2004 . The order of approximations for solutions of Ito-type stochastic differential equations with jumps . Stoch. Anal. Appl. 22 ( 3 ): 679 – 699 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 5 Kloeden , P.E. , and Platen , E. 1995 . Numerical Solutions of Stochastic Differential Equations . Springer-Verlag , Berlin . [Google Scholar]]. The Euler and the Milstein schemes are shown for finite and infinite Lévy measure.     

Periodic solutions for a kind of Liénard equation with two deviating arguments

In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Liénard equation with two deviating arguments of the form$x^{″}(t)+f(x(t))x^{\prime }(t)+g_1(t,x(t-{\tau }_1(t)))+g_2(t,x(t-{\tau }_2(t)))=p(t)\text{.}$