一类非线性中立型微分方程周期解的存在性

利用有关不等式,本文首先获得一类非线性中立型微分方程一个新的先验估计.基于解的先验估计以及迭合度理论,给出了这类中立型微分方程存在周期解的一个充分条件.     

On the stability of limit cycles for planar differential systems

We consider a planar differential system , , where P and Q are C¹ functions in some open set U⊆R², and . Let γ be a periodic orbit of the system in U. Let f(x,y):U⊆R²→R be a C¹ function such that

     

一类高阶中立型微分方程的最终正解的存在性

研究了一类高阶中立型泛函微分方程的最终正解的存在性,获得了其存在最终正解的充要条件.     

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．     

Existence and uniqueness of solutions for a second order differential equation with integral boundary conditions

In this paper, we consider the following second order differential equation

     

Existence theorem of periodic solutions for a delay nonlinear differential equation with piecewise constant arguments

Existence criteria are proved for the periodic solutions of a first order nonlinear differential equation with piecewise constant arguments.     

Pseudo almost periodic solutions for a class of first order differential iterative equations

This paper is concerned with a class of first order differential iterative equations. Under proper conditions, we employ a novel argument to establish a criterion on the existence of pseudo almost periodic solutions. The obtained result complements with some existing ones.     

Existence of periodic solutions for first order differential equations

In this paper we study the periodic boundary value problem for first order differential equations by combining techniques of the theory of differential inequalities, namely the method of upper and lower solutions, and the alternative method for nonlinear problems at resonance. The results obtained are in terms of the behavior of the nonlinear part at infinity.     

Periodic solutions of a second order forced sublinear differential equation with delay

In this paper, existence criteria are established for the existence of periodic solutions of a second order sublinear differential equation with delay and forcing function. Our method is based on careful a priori estimation and continuation theorems, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

Existence of periodic solutions for a class of first order delay differential equations dealing with vectors

By the weak linking theorem and the local linking theorem, we study the existence of periodic solutions for the following delay non-autonomous systems

(1)     

Generalized solutions to a linear discontinuous differential equation

In this paper we construct generalized solutions (weak solutions) to a linear discontinuous differential equation which appears as mathematical model in mechanics and for which usual methods are not quite adequate. The result is applied to the equation of an elastic beam on a Winkler type of foundation.     

Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations

By means of a monotone iterative technique, we establish the existence and uniqueness of the positive solutions for a class of higher conjugate-type fractional differential equation with one nonlocal term. In addition, the iterative sequences of solution and error estimation are also given. In particular, this model comes from economics, financial mathematics and other applied sciences, since the initial value of the iterative sequence can begin from an known function, this is simpler and helpful for computation.     

Turbulent solutions of a first order partial differential equation

A system of quasi-linear hyperbolic conservation laws which is hyperbolic but not strictly hyperbolic is studied. The system was derived as a model for the elastic string (B. Keyfitz and Kranzer, Arch. Rational Mech. Anal. 72 (1980), 210–241) and is assumed to be diagonizable. Interest is mainly in the large time behavior of the solution. Due to the nonlinearity of the system and the entropy condition, solutions converge to very simple elementary waves. Nonstrict hyperbolicity of the system may cause stronger nonlinear interactions between waves pertaining to different families; in particular, such interactions may regularize linear waves in the solution. The solutions are constructed using the random choice method.     

Three periodic solutions for a nonlinear first order functional differential equation

This paper is concerned with the existence of three positive T-periodic solutions of the first order functional differential equations of the form

x^′(t)=a(t)x(t)-λb(t)f(t,x(h(t))),     

Uniqueness of limit cycles for polynomial first-order differential equations

We study the uniqueness of limit cycles (periodic solutions that are isolated in the set of periodic solutions) in the scalar ODE in terms of {i_k}, {j_k}, {n_k}. Our main result characterizes, under some additional hypotheses, the exponents {i_k}, {j_k}, {n_k}, such that for any choice of the equation has at most one limit cycle. The obtained results have direct application to rigid planar vector fields, thus, planar systems of the form x^′=y+xR(x,y), y^′=−x+yR(x,y), where . Concretely, when the set has at least three elements (or exactly one) and another technical condition is satisfied, we characterize the exponents {i_k}, {j_k} such that the origin of the rigid system is a center for any choice of and also when there are no limit cycles surrounding the origin for any choice of .     

具偏差变元高阶Lienard方程周期解存在性

利用重合度理论,研究了一类具偏差变元高阶L ienard型方程周期解的存在性,获得了该方程至少存在一个周期解的充分条件.     

Periodic solutions of Abel differential equations

For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation.     

Analytic solutions of a second order iterative functional differential equation

This paper is concerned with an iterative functional differential equation

c₁x(z)+c₂x^′(z)+c₃x^″(z)=x(az+bx^′(z))