奇异半正边值问题正解的存在性

利用不动点指数定理,该文考虑了如下的三阶三点奇异半正边值问题 {x''(t)-f(t, x)=0,t ∈(0, 1); x(0)=x'(η)=x'(1)=0,1/2 <η <1, 多个正解的存在性.这里的非线性项 f (t, x) 可能在t =0,~ t =1和~ x =0处有奇性,并且可能在某些 t 和 x 处为负.     

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)     

Banach空间中非线性奇异两点边值问题的多重正解

本文研究Banach空间E中非线性奇异边值问题-x'=f(t,x), t∈(0,1), a₁x(0)-a₂x'(0)=θ, b₁x(0)-b₂x'(1)=θ.其中θ是E中的零元素, f({t,x})在端点t=0和t=1处具有奇性. 利用不动点定理获得了该问题至少有两个正解的结果.     

具p-Laplacian算子型奇异方程组边值问题正解的存在性

本文讨论了一类具p-Laplacian算子型奇导方程组边值问题(φp(x'))'+α1(t),f(x(t),y(t))=0,(φp(y'))'+α2(t)g(x(t),y(t))=0,x(0)-β1x'(0)=0,x(1)+δ1x'(1)=0,y(0)-β2Y'(0)=0,y(1)+δ2y'(1)=0正解的存在性,其中φp(x)=|x|p-2x,p>1.通过使用不动点指数定理,在适当的条件下,建立了这类奇异方程组边值问题存在一个或者多个正解的充分条件.这些结果能用来研究椭圆型方程组边值问题径向对称解的存在性.     

STABILITY AND EXISTENCE OF PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS ON LIENARD SYSTEMS

1MainResultsConsidersystem11~.x f(x)x' g(x)~0(1)wheref(x)islocallyintegrable,g(x)isdifferentiablealldg(0)=0.Theroem1Thezerosolutionofsystem(1)isuniformlyasymptoticallystableifbyequivalenttransf'Ormu=xov=X' F(x).DefineW[t,(uif\v)]j6ug(s)ds Iv',thenwisaposi…     

二阶具和不具时滞的微分方程解的有界性和稳定性

本文利用一类新的推广了的积分不等式和文[1,7]提供的方法,得到了判别二阶常微分方程(a(t)x')'+f(t,x)=0和二阶时滞微分方程(a(t)x')'+F(t,x(t),x(t-τ)(t)))=0解的有界性和稳定性的充分条件。     

Roughness of Exponential Estimates for Linear Functional Differential Equations

<正> Assume that the fundamental solution matrix U (t, s ) of x'(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ   

含有各阶导数的四阶两点边值问题正解的存在性

利用一个新的锥不动点定理,研究含有各阶导数四阶两点边值问题{x~((4))(t)+Ax'(t)=λf(t,x(t),x'(t),x'(t),x''(t)),0t1 x(0)=x(1)=x'(0)=x'(1)=0正解的存在性.其中f是一个非负连续函数,λ0,0Aπ~2.     

共振条件下四阶四点边值问题的可解性

本文讨论四阶常微分方程$x^{(4)}(t)=f(t,x(t),x'(t),x'(t),x'(t)),\;\;\;t\in(0,1), \eqno (E)$在边值条件$x(0)=x(1)=0,\;\alpha x'(\xi_1)-\beta x'(\xi_1)=0,\;\gamma x'(\xi_2)+\delta x'(\xi_2)=0, \eqno(B)$满足共振情形: $\alpha \delta+\beta\gamma+\alpha\gamma(\xi_2-\xi_1)     

二阶拟线性微分方程组边值问题的三个对称正解

本文讨论二阶拟线性微分方程组边值问题( p(x'))'+a(t),(t,x,y)=0,( q(y'))'+b(t)g(t,x,y)=0,x(0)-B0(x'(0))=x(1)+Bo(x'(1))=0,y(0)-B1(y'(0))=y(1)+B1(y'(1))=0,其中f,g是非负连续的函数.利用五个泛函的不动点定理,赋予f和g一些增长条件保证至少三个对称正解的存在性.