Homoclinic Orbits for Second Order Discrete Hamiltonian Systems with Potential Changing Sign

In this paper, a class of second order discrete Hamiltonian systems without any periodicity assumptions are considered. Base on the critical point theory, some sufficient conditions for the existence of homoclinic orbits are obtained. The results obtained extend the results in [2006] by relaxing the assumptions on the sign of the potential.      

Periodic Solutions of Nonautonomous Second Order Hamiltonian Systems

In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems （H） ü＋A（t）u＋∨V（t, u）=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.     

On the Viscosity Solutions for Nonlinear Systems of Second Order Elliptic Equations

ＯｎｔｈｅＶｉｓｃｏｓｉｔｙＳｏｌｕｔｉｏｎｓｆｏｒＮｏｎｌｉｎｅａｒＳｙｓｔｅｍｓｏｆＳｅｃｏｎｄＯｒｄｅｒＥｌｉｐｔｉｃＥｑｕａｔｉｏｎｓＬｉｕＷｅｉａｎ（刘伟安）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ，Ｈｕｂｅｉ...     

Research Announcements Oscillon of Second Order Matrix Differntial Systems

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＯｓｃｉｌｌａｔｉｏｎｏｆＳｅｃｏｎｄＯｒｄｅｒＭａｔｒｉｘＤｉｆｆｅｒｅｎｔｉａｌＳｙｓｔｅｍｓＭｅｎｇＦａｎｗｅｉ（孟凡伟）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｓｈａｎ...     

Multiple Periodic Solutions with Minimal Period for Second Order Discrete System

By making use of Clark duality, minimax theory and geometrical index theory, some results on the existence and multiplicity of subharmonic solutions with prescribed minimal period to second order subquadratic discrete system are obtained.     

Convergence of a Time Discretisation for Doubly Nonlinear Evolution Equations of Second Order

The convergence of a time discretisation with variable time steps is shown for a class of doubly nonlinear evolution equations of second order. This also proves existence of a weak solution. The operator acting on the zero-order term is assumed to be the sum of a linear, bounded, symmetric, strongly positive operator and a nonlinear operator that fulfils a certain growth and a Hölder-type continuity condition. The operator acting on the first-order time derivative is a nonlinear hemicontinuous operator that fulfils a certain growth condition and is (up to some shift) monotone and coercive.     

Dynamical Behavior in Behavior in Simple and Coupled Systems of Continuous Josephson－Junctions

ＤｙｎａｍｉｃａｌＢｅｈａｖｉｏｒｉｎＢｅｈａｖｉｏｒｉｎＳｉｍｐｌｅａｎｄＣｏｕｐｌｅｄＳｙｓｔｅｍｓｏｆＣｏｎｔｉｎｕｏｕｓＪｏｓｅｐｈｓｏｎ－ＪｕｎｃｔｉｏｎｓＱｉａｎＭｉｎ（钱敏）ＺｈｏｕＳｈｅｎｇｆａｎ（周盛凡）（ＤｅｐａｒｔｍｅｎｏｆＭａ...     

Interior C 1, γ-Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems

The interior C ^{γ, γ/2}-regularity for the first gradient with respect to the space variables of a weak solution to a class of nonlinear second order parabolic systems is proven under the assumption that oscillations of coefficients are controlled by the ellipticity constant.     

Dynamical Behavior for the Three-dimensional Generalized Hasegawa-Mima Equations

We consider the following generalized three-dimensional (3-D) dissipative Hasegawa-Mima equations:     

Structure-Preserving Algorithms for a Class of Dynamical Systems

In this paper,we study structure-preserving algorithms for dynamical systems defined by ordinarydifferential equations in R~n.The equations are assumed to be of the form y~·=A(y) D(y) R(y),where A(y)is the conservative part subject to     

Hopf Bifurcation for Non—smooth Planar Dynamical Systems

The purpose of this paper is to study the Hopf bifurcation property of the non-smooth planar dynamical systemwhere the individual functions K± R2 x I R2 at the right-hand side for some interval I containing 0 are smooth enough and given byThe parameter dependent matrices Aa(A) are assumed to be of the formwhere a 0 and w±() > 0. And the nonlinear terms in equation (??) are assumed to be smooth enough and have the formIn a standard way we extend the system (??) to a differential inclusion …     

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-…     

Global Estimates for Green’s Matrix of Second Order Parabolic Systems with Application to Elliptic Systems in Two Dimensional Domains

We establish global Gaussian estimates for the Green’s matrix of divergence form, second order parabolic systems in a cylindrical domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate and a local Hölder estimate. From these estimates, we also derive global estimates for the Green’s matrix for elliptic systems with bounded measurable coefficients in two dimensional domains. We present a unified approach valid for both the scalar and vectorial cases and discuss several applications of our result.     

Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems

By means of the theory on the semi-global C1 solution to the mixed initial-boundary value problem (IBVP) for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.     

On Eigenvalue Intervals for Discrete Second Order Boundary Value Problems

In this paper, we consider discrete second order three-point boundary value problems. By exploring the properties of the associated Green's function and applying Guo-Krasnosel'skii's fixed point theorem, we show the existence of eigenvalue intervals.     

Martelli’s Chaos in Inverse Limit Dynamical Systems and Hyperspace Dynamical Systems

In this paper we investigate Martelli’s chaos of inverse limit dynamical systems and hyperspace dynamical systems which are both induced from dynamical systems on a compact metric space. We give the implication of Martelli’s chaos among those systems. More precisely, we show that inverse limit dynamical system is Martelli’s chaos if and only if so is original system, and we prove that hyperspace dynamical system is Martelli’s chaos implies original system is Martelli’s chaos if the orbit of every single point set of original system is unstable in hyperspace dynamical system.     

Homoclinic Orbits for Second Order Hamiltonian System with Quadratic Growth

ＨｏｍｏｃｌｉｎｉｃＯｒｂｉｔｓｆｏｒＳｅｃｏｎｄＯｒｄｅｒＨａｍｉｌｔｏｎｉａｎＳｙｓｔｅｍｗｉｔｈＱｕａｄｒａｔｉｃＧｒｏｗｔｈＷｕＳｈａｏｐｉｎｇ（吴绍平）（Ｍａｔｈ．Ｄｅｐｔ．ＺｈｅｊｉａｎｇＵｎｉｖ．，Ｈａｎｇｚｈｏｕ，Ｚｈｅｊｉａｎｇ，３...     

Dynamical behavior for an eco-epidemiological model with discrete and distributed delay

In this paper, the dynamical behavior of an eco-epidemiological model with discrete and distributed delay is studied. Sufficient conditions for the local asymptotical stability of the nonnegative equilibria are obtained. We prove that there exists a threshold value of the feedback time delay τ beyond which the positive equilibrium bifurcates towards a periodic solution. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.     

Riemann—Hilbert Problem for the First Order Elliptic Systems

In this article we discuss the Riemann—Hilbert problems for the first order elliptic systems and prove the existence of the solution by means of general analytic function theory and Cauchy integral formula.     

Notes on Oscillation of Solution for aCertain Second Order Neutral Equation

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃｏｎｓｉｄｅｒｏｓｃｉｌｌａｔｏｒｙｏｆｅｑｕａｔｉｏｎ（１）［ｘ（ｔ）＋ｃｘ（ｔ－τ）］″＋∫ｂａｐ（ｔ，ξ）ｘ［ｇ（ｔ，ξ）］ｄσ（ξ）＝０，（１）ｗｈｅｒｅτ０；ｐ（ｔ，ξ），ｇ（ｔ，ξ）∈Ｃ（［ｔ０，＋∞）×［ａ，ｂ］，Ｒ）；ｇ（ｔ，ξ）ｔ，ξ∈［ａ，ｂ］；ｇ（ｔ，ξ）ａｒｅｎｏｎ－ｄｅｃｒｅａｓｉｎｇｗｉｔｈｔｏｔ，ξ，ｒｅｓｐｅｃｔｉｖｅｌｙａｎｄｌｉｍｔ→＋∞ｍｉｎξ∈［ａ，ｂ］｛ｇ（ｔ，ξ）｝＝＋∞，σ（ξ）∈（［ａ，ｂ］，Ｒ）ｉｓｎｏｎｄｅｃｒ…