一类延迟积分方程的渐近概周期解

积分方程解的性态是积分理论中一个重要而又基本的问题.其中关于方程的周期解、概周期型解的存在性问题更是具有重要的理论意义和应用价值.已有文献中,有的延迟是常数,而有的延迟虽为函数,但对延迟做了是概周期函数的假设.本文在某些延迟积分方程的概周期解的存在性的基础上,并利用渐近概周期函数的定义和不动点理论,讨论了一类延迟是渐近概周期函数的积分方程的渐近概周期解的存在性.     

Multiplicity of Periodic Solutions of Duffing Equations with Jumping Nonlinearities

We provide sufficient conditions for the existence and multiplicity of subharrnonic solutions for Duffing's equations with jumping nonlinearities.     

带梯度算子二阶方程的渐近概周期解

利用渐近概周期函数的性质得到带梯度算子二阶方程的渐近概周期解在C（R^-）中的存在性．同时利用迭代法和线性常微分方程的概周期解的存在性和唯一性,得到R上此方程渐近概周期解的存在和唯一性．     

Nontrivial Solutions for One-Dimensional Fourth-Order Kirchhoff-Type Equations

Using variational methods and critical point theory, we establish multiplicity results of nontrivial solutions for one-dimensional fourth-order Kirchhoff-type equations.     

一类具有逐段常变量微分方程的渐近概周期解

利用差分方程的渐近概周期序列解,讨论了一类具有逐段常变量微分方程的渐近概周期解的存在性．     

一类非线性微分方程渐近概周期解的存在性

利用函数的遍历性和耗散型条件,研究一类非线性微分方程渐近概周期解的存在性．在某些特定的条件下,得到了这类方程渐近概周期解存在性和唯一性结论．从而得到的结果在一定程度上推广和改进了相关结果．     

Existence and Multiplicity of Periodic Solutions of the Second-Order Differential Equations with Jumping Nonlinearities

We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping nonlinearities under resonance conditions. Received March 1, 1999, Revised September 16, 1999, Accepted February 1, 2000     

Existence of Nodal Solutions for Dirac Equations with Singular Nonlinearities

We prove, by a shooting method, the existence of infinitely many solutions of the form ${\psi (x^{0}, x) = {{e}}^{-i \Omega x^{0}} \chi(x)}$ of the nonlinear Dirac equation $$i \underset{\mu = 0}{\overset{3}{\sum}}\gamma^{\mu} \partial_\mu \psi-m \psi - F( \overline{\psi}\psi)\psi = 0$$ where Ω >  m >  0, χ is compactly supported and $$F(x) = \left \{\begin{array}{ll}{p|x|^{p-1}} & {\rm if} |x| > 0\\ 0 & {\rm if} x = 0 \end{array}\right.$$ with ${p \in (0,1)}$ under some restrictions on the parameters p and Ω. We study also the behavior of the solutions as p tends to zero to establish the link between these equations and the M.I.T. bag model ones.     

Standing Waves for Periodic Discrete Nonlinear SchrSdinger Equations with Asymptotically Linear Terms

In this paper we study the existence of nontrivial solutions for the periodic discrete nonlinear equation Lun ωun = fn(un), where Lun = a n+1un+1 + an1un1+ bnun is the discrete Laplacian in one spatial dimension. The given real-valued sequences an , bn are assumed to be N -periodic in n, i.e., an+N = an , b n+N = bn . The nonlinearity fn(t) is N-periodic in n and asymptotically linear at infinity. We show that, if ω is in the spectrum gap of L, there is a nontrivial solution. The proof is based on the strongly indefinite functional critical points theorem developed recently.     

Localization of Closed (or Periodic) Solutions of a Differential System with Concave Nonlinearities

Consider a scalar differential equation , where I is an open interval containing [0,T]. Assumethat f(t, x) is continuous with a continuous derivative , and weakly concave (or weakly convex)in x for all t I, though strictly concave (or strictly convex)for some t [0, T]. It is well known that in this case therecan be either no, one or two closed solutions; that is, solutions(t) for which (0) = (T) If there are two closed solutions, thenthe greater has a negative characteristic exponent and the smallerhas a positive one. It is easily seen that this is equivalentto a statement on localization of closed solutions. It is shownhow this statement can be generalized to systems of differentialequations . The requirements are that the coordinate functions ) be continuous with continuous derivatives with respect to x₁,x₂, ...,x_n, that the f_j are weakly concave (or weakly convex)in , and that a certain condition pertaining to strict concavity (or strict convexity) is fulfilled.2000 Mathematics Subject Classification 34C25, 34C12.     

Periodic Solutions for Nonlinear Diferential Equations

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Infinitely Many Solutions of Nonlocal Kirchhoff-Type Equations via Perturbation Methods

Mathematical Notes - We study the multiplicity of weak solutions to the boundary-value problem $$begin{alignedat}{2} - Mbiggl(iint_{mathbb R^{2N}}|u(x)-u(y)|^2 K(x-y),d x,d ybiggr)mathscr...     

Fourier-Galerkin Method for Localized Solutions of Equations with Cubic Nonlinearity

Using a complete orthonormal system of functions in L ²(– ,) a Fourier-Galerkin spectral technique is developed for computing of the localized solutions of equations with cubic nonlinearity. A formula expressing the triple product into series in the system is derived. Iterative algorithm implementing the spectral method is developed and tested on the soliton problem for the cubic Boussinesq equation. Solution is obtained and shown to compare quantitatively very well to the known analytical one. The issues of convergence rate and truncation error are discussed.     

Criteria for the Trivial Solution of Differential Algebraic Equations with Small Nonlinearities to be Asymptotically Stable

Differential algebraic equations consisting of a constant coefficient linear part and a small nonlinearity are considered. Conditions that enable linearizations to work well are discussed. In particular, for index-2 differential algebraic equations, there results a kind of Perron Theorem that sounds as clear as its classical model.     

非自治时滞微分方程的正周期解

By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.     

时滞Rayleigh方程周期解问题

利用Mahwin重合度拓展定理研究了一类具时滞Rayleigh方程x″(t)+f(x′(t))+g∫0-rx(t+s)dm(s)=p(t)周期解问题,得到了周期解存在的一组充分条件.     

First Integrals and Periodic Solutions of a System with Power Nonlinearities

Under consideration is some system of ordinary differential equations with power nonlinearities. These systems are widely used in mathematical biology and chemical kinetics, and can also occur by reduction of more sophisticatedmodels. We formulate conditions on the system parameters which guarantee the existence of first integrals defined by the combinations of power and logarithmic functions of the phase variables. Using the first integrals, we construct periodic solutions for the three-variable systems. A few examples are given illustrating the results.