Remark on Krasnosielski’s guiding functions and Srzednicki’s periodic segments

We show that the existence of the complete set of guiding functions guarantees the existence of periodic isolating segment that carries the same information concerning periodic solutions of the non-autonomous periodic equations x^′=f(x,t)$x^{\prime }=f(x,t)$.     

Existence of infinitely many periodic solutions for ordinary p-Laplacian systems

In this paper, we study the existence and multiplicity of non-trivial periodic solutions of ordinary p-Laplacian systems by using the minimax technique in critical point theory. We also give an example to illustrate that the obtained results are new even in the case p=2.     

Weak singularities may help periodic solutions to exist

In a periodically forced semilinear differential equation with a singular nonlinearity, a weak force condition enables the achievement of new existence criteria through a basic application of Schauder's fixed point theorem. The originality of the arguments relies in that, contrary to the customary situation in the available references, a weak singularity facilitates the arguments of the proofs.     

Existence of multiple positive periodic solutions for functional differential equations

In our paper, by employing Krasnoselskii fixed point theorem, we investigate the existence of multiple positive periodic solutions for functional differential equations

     

The existence of periodic solutions of higher order nonlinear periodic difference equations

Sufficient conditions for the existence of at least one periodic solution of two classes of nonlinear higher order periodic difference equations are established, respectively. The results show us that sufficient conditions for the existence of T ? periodic solutions of difference equation are different from those ones for the existence of T ? periodic solutions of differential equation. Copyright © 2012 John Wiley & Sons, Ltd.     

非自治时滞微分方程正周期解的存在性

应用Krasnoselskii锥映射不动点定理，研究了具一般时滞非线性非自治Logistic方程的ω-周期解的存在性，获得了存在正周期解的充分条件．     

Periodic solutions of a periodic delay predator-prey system

The existence of a positive periodic solution for

is established, where , , , , are positive periodic continuous functions with period , and , are periodic continuous functions with period .

     

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.     

Periodic solutions of a class of superquadratic second order Hamiltonian systems

§1　IntroductionInthispaperwediscusstheexistenceofthesolutionforthefollowingsecondorderHamiltoniansystemx¨ Ax ΔF(x)=0,(1.1)whereAisann×nrealsymmetricmatrixandisnon-definite,F∈C1(Rn,R),andΔF(x)denotesthegradientofF.WhileworksforsecondorderHamiltonsystemshavemostlybeendoneundertheconditionA=0,westudythecasewhereA≠0andisnon-definiteinthepapers[1,2].DefineH=H1,2T([0,T],Rn)={x:R→Rn|xisabsolutelycontinuous,x∈L2([0,T],Rn),x(0)=x(T),x(0)=x(T)}and〈x,y〉=∫T0[(x(t),y(t)) (x…     

Periodic solutions of delay impulsive differential equations

We study the following semilinear impulsive differential equation with delay:

     

Banach空间四阶周期边值问题正解的存在性

讨论了Banach空间E中的四阶周期边值问题:( u(4)(t)??u00(t)+′u(t)= f(t; u(t));06 t 61; u(i)(0)= u(i)(1); i =0;1;2;3正解的存在性,其中f :[0;1]￡ P ! P连续, P为E的正元锥,?;′2 R且满足0<′<(?2+2?2)2;?>?2?2;′?4+??2+1>0:通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果.     

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…     

周期系数Ricatti方程之周期解

本文利用Brouwer不动定理，研究了Ricatti方程的周期解的存在性。     

二次周期系数微分方程的周期解

给出利用Schauder不动点定理求一类二次周期系数微分方程的周期解的一种方法,得到较好结果.     

Positive periodic solutions of higher-dimensional nonlinear functional difference equations

By using a well-known fixed point index theorem, we study the existence, multiplicity and nonexistence of positive T-periodic solution(s) to the higher-dimensional nonlinear functional difference equations of the form

     

一类具周期系数的Riccati型方程的周期解

给出 Riccati型方程x=A( t) x2 m+B( t) x2 k- 1 +C( t)( A( t) ,B( t) ,C( t)是周期为 T的连续函数 ,m,k∈ N且 m≥ k)无周期解及存在周期解的充分条件 .     

On the maximum number of periodic solutions of piecewise smooth periodic equations by average method

In this paper, we prove smoothness of bifurcation function for a piecewise smooth periodic equation, and then use the bifurcation function together with its smoothness to study the maximum number of periodic solutions of the piecewise smooth periodic equation by the first order average.