Localization of the method of guiding functions in the problem about periodic solutions of differential inclusions

In this paper we consider the problem on the existence of forced oscillations in nonlinear objects governed by differential inclusions. We propose certain modifications of the methods of generalized and integral guiding functions.     

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))),     

On the existence of periodic solutions for differential inclusions

In this paper we study the existence of periodic solutions for differential inclusions. We prove existence theorems under various sets of hypotheses for both the nonconvex and convex problems. Also we show the existence of extreme solutions. Some feedback control systems are also considered.     

Numbers of subnormal solutions for higher order periodic differential equations

In this paper, we estimate the number of subnormal solutions for higher order linear periodic differential equations, and estimate the growth of subnormal solutions and all other solutions. We also give a representation of subnormal solutions of a class of higher order linear periodic differential equations.     

Periodic solutions for a class of differential inclusions in general Banach spaces

Let X be a real Banach space, an m-accretive operator and a multi-function which is 2π-periodic with respect to its first argument, has nonempty, closed, convex and weakly compact values and is strongly-weakly upper semicontinuous. In this paper we prove the existence of at least one solution for the problem

     

Bifurcation of periodic solutions with large periods for a delay differential equation

We consider a one-parameter family of delay differential equations which has been proposed as a model for a prize and prove that at a critical parameter where the linearization at equilibrium has a double zero eigenvalue periodic solutions bifurcate off with periods descending from infinity. AMS Subject Classification. 34K18,34K13,37G15     

Bifurcations of periodic solutions of delay differential equations

In this paper we develop Kaplan-Yorke's method and consider the existence of periodic solutions for some delay differential equations. We especially study Hopf and saddle-node bifurcations of periodic solutions with certain periods for these equations with parameters, and give conditions under which the bifurcations occur. We also give application examples and find that Hopf and saddle-node bifurcations often occur infinitely many times.     

Lyapunov exponents of solutions to linear differential equations with periodic forcing functions

We give Lyapunov exponents of solutions to linear differential equations of the form x^′=Ax+f(t), where A is a complex matrix and f(t) is a τ-periodic continuous function. Notice that f(t) is not “small” as t→∞. The proof is essentially based on a representation [J. Kato, T. Naito, J.S. Shin, A characterization of solutions in linear differential equations with periodic forcing functions, J. Difference Equ. Appl. 11 (2005) 1-19] of solutions to the above 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.     

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

In this paper, we employ a well-known fixed-point index theorem to study the existence and non-existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. Several existence and non-existence results are established.     

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.     

Nontrivial periodic solutions for delay differential systems via Morse theory

The existence of the nontrivial periodic solutions to the system of delay differential equations

(1.1)     

Existence of multiple solutions for a wide class of differential inclusions†

We give a unified approach to study the existence of multiple positive solutions of nonlinear differential inclusions of the form $$-u^{\prime \prime }(t)\in F(t,u(t)),\text{a.e.}t\in (0,1),$$ subject to various nonlocal boundary conditions. We study these problems via a perturbed integral inclusion of the form $u(t)\in Bu(t)+{\int }_0^{1}k(t,s)F(s,u(s))ds$.     

On a class of implicit differential inclusions

The existence of solutions is established for implicit differential inclusions in involving the sum of a maximal monotone mapping and an upper semicontinuous mapping with compact, closed values. A question of Wenzel is answered in the affirmative.

     

Existence of periodic solutions for neutral functional differential equations with nonlinear difference operator

In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.     

具偏差变元的高阶中立型泛函微分方程的周期解存在性问题

利用 Fourier 级数理论,伯努利数理论和重合度理论研究了一类具偏差变元的高阶中立型泛函微分方程的周期解问题,得到了周期解存在的充分条件.