Oscillations of Second Order Nonlinear Neutral Differential Equations

ＯｓｃｉｌｌａｔｉｏｎｓｏｆＳｅｃｏｎｄＯｒｄｅｒＮｏｎｌｉｎｅａｒＮｅｕｔｒａｌＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓＷａｎｄＯｉｒｕ；（王其如）ＷｕＹｅｗｅｉ（武业伟）（ＬｕｏｇａｎｇＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，Ｌｕｏｙａｎｇ４７１０２...     

On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order

We deal with the existence of periodic solutions for doubly degenerate quasilinear parabolic equations of higher order, which can degenerate, on a part of the boundary, on a segment in the interior of the domain and in time.     

Nonlocal Boundary Conditions for Higher–Order Parabolic Equations

This work deals with the efficient numerical solution of the two–dimensional one–way Helmholtz equation posed on an unbounded domain. In this case one has to introduce artificial boundary conditions to confine the computational domain. Here we construct with the Z –transformation so–called discrete transparent boundary conditions for higher–order parabolic equations schemes. These methods are Padé “Parabolic” approximations of the one–way Helmholtz equation and frequently used in integrated optics and (underwater) acoustics. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Painlevé Analysis of Higher Order Nonlinear Evolution Equations with Variable Coefficients

There is a close relationship between the Painlevé integrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)...     

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

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

Multi-Level Spliting Methods Solving Difference Equations

Ｍｕｌｔｉ┐ＬｅｖｅｌＳｐｌｉｔｉｎｇＭｅｔｈｏｄｓＳｏｌｖｉｎｇＤｉｆｅｒｅｎｃｅＥｑｕａｔｉｏｎｓ＊）ＬｉＦｅｎｇ（李锋）ＬｉＲｏｎｇｈｕａ（李荣华）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕ...     

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     

On Monotone Method for Second Order Periodic Boundary Value Problems and Periodic Solutions of Functional Difference Equations

In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution a and upper solution βwith α≤β.     

Second Order Complex Equations of Mixed Type

ＳｅｃｏｎｄＯｒｄｅｒＣｏｍｐｌｅｘＥｑｕａｔｉｏｎｓｏｆＭｉｘｅｄＴｙｐｅＳｕｎＨｅｓｈｅｎｇ（孙和生）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓ）Ｐ．Ｏ．Ｂｏｘ８００９，Ｂｅｉｊｉｎ...     

Statistical Convergence of Order α for Difference Sequences

Abstract

In this paper the concepts of ?^m_v-statistical convergence of order α and strong (p, ?^m)-Ces`aro summability of order α are introduced for sequences of complex (or real) numbers. Some relations between the ?<sup>m</sup><sub>v</sub>-statistical convergence of order α and strong (p, ?<sup>m</sup><sub>v</sub>)-Ces`aro summability of order α are given. Also some relations between the space ω^α_p (?^m_v, f) and S^α (?^m_v) are examined.     

Bounded Perturbations of Second Order Ordinary Differential Equations

In the studying of the non-dissipative systems,the following periodic boundaryvalue problemsplay a very important role.where p(t)is 2 π-periodic and continuous,g∈C'(R),xg(x)>0(x≠0).Some existence results were obtained under various additional as-     

On the Oscillation of the Fourth Order Differential Equations

61.IntroductionWeconsiderthefourthorderdifferentialequationx(`)(t)-p(t)lx(t)I'sgnx(t)=O,(1.l)wherea>l,isconstant,andp(t)ispositivecontinuousfunctionon[t,,oo),to>o.Werestrictourattentiontothosenontrivialsolutionsx(t)of(1.1)whichexistonsomehalf-[ine[T:,co)cy[t,,oo),suchasolutioniscalledapropersolutionof(1.l).ApropersolutioniscalledoscillatoryifithasarbitrarilylargezerosFotherwiseitiscallednonoscillatory.Wecon-sidertheoscillationandnonoscillationofpropersolutionsof(l,l).WeletEdenotethesetofall…     

An Oscillation Criterion for Second Order Superlinear Differential Equations

61.IntroductionConsiderthesecondordersuperlinearequationx'(t) p(t)X'(t) q(t)1x(t)l"sgnx(t)=o,t>to,(1)wherea>l,pandq:[t,'co)-R=(-co,oo)arecontinuous.Weconsideronlysuchsolutionsxofequation(l)whichexistonsomeinterval[t.,oo),t.>t,>o.Asolutionofequation(l)issaidtobeoscillatoryifithasarbitrarilylargezerosandotherwise,itissaidtobenonoscillatory.Equation(l)iscalledoscillatoryifallofitssolutionsareoscilllatory.Forthespecialcasewherep(t)=Oli.e.,forthedifferentialequationx'(t) q(t)lx(t)l"sgnx(t)=o,a>1-…     

Boundary Value Problems for First Order Stochastic Differential Equations

In this paper, we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition （in the sense of expectation）. Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value. Then by using the contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the existence theorem. Finally, we explain our main results by an elementary example.     

Sufficient Conditions for the Oscillation of Non-autonomous Difference Equations

Abstract In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous differenceequations x(n 1)-x(n) sum from i=1 to m p_i(n)x(n-r_i(n))=0,which are the discrete analog of the delay differential equations considered in[1].     

Quasi-periodic Solutions of Nonlinear Schrodinger Equations of Higher Dimension

We are concerned with the existence of the quasi-periodic solutions of the nonlinear Schr(?)dinger（NLS）eauationwhere △ is the　d-Laplace and　Mσ is a Fourier multiplier,i.e,     

Oscillations of the Solutions of Nonlinear Delay Hyperbolic Partial Differential Equations

In this paper, oscillatory properties of solutions of certain hyperbolic partial differential equations with multi-delays are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delays.     

Evolution Hemivariational Inequality with Hysteresis Operator in Higher Order Term

The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the use of the time-discretization procedure.