Solvability of Boundary Value Problems for Some Functional Differential Equations

This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, xt) (0相似文献   

Positive solutions for some 1-dimensional boundary value problems of Laplace-type

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type(φ(x'(t)))' q(t)f(t,x(t),x'(t)) = 0, t ∈ (0, 1),subject to the following boundary condition:a1φ(x(0)) - a2φ(x'(0)) = 0, a3φ(x(1)) a4φ(x'(1)) = 0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem,sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.     

Cubic Lienard equation with quadradic damping (I)

1. IntroductionLienard equationdZx dx~ f(.)g g(x) = 0 (l.0)dtZ dthas been extensively studied with particular emphasis on the ekistence and uniqueness oflimit cycles (see e.g. [l--4] and references there in). The number of limit cycles of (l.0) hasbeen also investigated by several authors (see e.g. [5--8]).In the present paper we study the general cubic Lienard equation, namelydx da~ = y ~ F(x), Z ~ ~g(x) (1.1)dt' dtwhereF(x) = ale a,x: a,x', (l.2)g(x) = blx b,x' b,x'. (1.3)Clea…     

依赖于导数项的非对称振子解的无界性（英文）

In this paper, we consider the unboundedness of solutions for the asymmetric equation x'+ax~+-bx~-+(x)ψ(x')+f(x)+g(x')=p(t),where x~+= max{x, 0}, x~-= max{-x, 0}, a and b are two different positive constants,f(x) is locally Lipschitz continuous and bounded, (x), ψ(x), g(x) and p(t) are continuous functions, p(t) is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions: the resonance case 1/a~(1/2)+1/b~(1/2)∈Q and the nonresonance case 1/a~(1/2)+1/b~(1/2)?Q     

三阶奇异边值问题的正解

本文在较弱的条件下,研究了三阶奇异边值问题{x'+a(t)F(t,x)=0 0＜t＜1,x(0)=x'(0)=x(1)=0正解的存在性.允许非线性项a(t),F(t,x)在t=0,t=1及x=0处奇异.     

一类具偏差变元的二阶微分方程周期解

By using the theory of coincidence degree,we study a kind of periodic solutions to second order differential equation with a deviating argument such as x"(t) f(x'(t)) h(x(t))x'(t) g(x(t-τ(t)))=p(t),some sufficient conditions on the existence of periodic solutions are obtained.     

EXPONENTIAL FITTED METHODS FOR THE NUMEMCAL SOLUTION OF THE SCHRDINGER EQUATION

1.IntroductionInrecelltyearstheSchr5dingerequationhasbeenthesubectofgreatactivity,thealmist0aChieveafastandreliablealgorithmthatgeneratesanumericalsohiion.1.1.~ialSchr5dingerequati0nTheonedimensionalorradialSchrwhngerequati0nhastheform:y"(x)=ll(l+1)/x'+V(x)-k'1y(x).(1)whereoneboundaryc0nditionisy(0)=Owiththe0therboundaryconditionbe-ingspeciliedatx=oo.Equati0nsofthistyPeoccuxveryfrequentlyintheOreticalphysicsIs],andthereisareaJneedtobeabletosolvethembothefficientlyandreliablybynumericalmeth…     

OSCILLATORY AND ASYMPTOTIC BEHAVIORS OF FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper the author discusses the following first order functional differentialequations: x'(t) +integral from n=a to b p(t, ξ)x[g(t, ξ)]dσ(ξ)=0, (1) x'(t) +integral from n=a to b f(t, ξ, x[g(t, ξ)])dσ(ξ)=0. (2)Some suffcient conditions of oscillation and nonoseillafion are obtained, and two asymptolioproperties and their criteria are given. These criferia are better than those in [1, 2], and canbe used to the following equations: x'(t) + sum from i=1 to n p_i(t)x[g_i(t)] =0, (3) x'(t) + sum from i=1 to n f_i(t, x[g_i(t)] =0. (4)     

共振条件下多点边值问题解的存在性

本文讨论多点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1);x'(0)= x'(ξ),x(1)=sum from i=1 to m-3βix(ηi)解的存在性,其中βi∈R,sum from i=1 to m-3β=1,0<η1<η2< …<ηm-3<1,0<ξ<1,sum from i=1 to m-3βiηi=1.这时dimKer L=2.当βi取不同的符号 时,应用Mawhin重合度定理,证明了多点边值问题的一些存在性结果. 以前文章所 涉及的多点边值问题解的存在性都是在dim Ker L=1的情况下讨论的,所以我们的 工作是新的探索.     

Some oscillation criteria for second order nonlinear functional ordinary differential equations

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) ＞ 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.