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2005年01月26日

【期刊论文】Multiplicity results for some second-order four-point boundary-value problems☆

葛渭高， Zhanbing Bai a， b， *， Weigao Gea， YifuWang a

Nonlinear Analysis 60(2005)491-500，-0001，（）：

-1年11月30日

In this paper, by using a fixed point theorem of functional type in a cone, some new results for the multiplicity ofpositi ve solutions ofsecond-order four-point boundary-value problems are obtained. The emphasis is put on the nonlinear term involved with the first-order derivative.

Fixed point theorem， Positive solution， Multiplicity， Boundary value problem

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2005年01月26日

【期刊论文】Solvability of nonlocal boundary value problems for ordinary differential equations of higher order☆

葛渭高， Yuji Liu a， b， *， Weigao Ge a

Nonlinear Analysis 57(2004)435-458，-0001，（）：

-1年11月30日

摘要

In this paper, we prove existence results for a nonlocal boundary value problem concerning a higher order di#erential equation. Our method is based upon the coincidence degree theory of Mawhin. The interesting point is that the degree of some variables among x0,x1,……xn−1 in the function f(t,x0, x1,……xn−1) are allowable to be greater than 1. Some examples are given to illustrate the main results.

Nonlocal boundary value problem， Boundary value problem at resonance， Solvability， Higher order differential equation

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2005年01月26日

【期刊论文】On a third-order multi-point boundary value problem at resonance✩

葛渭高， Zengji Du a， *， Xiaojie Lin b， Weigao Ge a

J. Math. Anal. Appl. 302(2005)217-229，-0001，（）：

-1年11月30日

摘要

In this paper, we prove some existence results for a third order multi-point boundary value problem at resonance. Our method is based upon the coincidence degree theory of Mawhin.

Multi-point boundary value problem， Resonance， Coincidence degree theory， Third-order differential equations

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2005年01月26日

【期刊论文】Solutions of 2nth Lidstone boundary value problems and dependence on higher order derivatives✩

葛渭高， Zhanbing Bai a， b， * and Weigao Ge a

J. Math. Anal. Appl. 279(2003)442-450，-0001，（）：

-1年11月30日

摘要

In this paper, we consider the Lidstone boundary value problem (−1)nu(2n)(x)=f (x,u(x),u''(x),……,u(2(n−1))(x)), 0<x<1, u(2i)(0)=u(2i) (1)=0, 0≤i≤n−1. Some monotone conditions are imposed on f which enable us to apply a new maximum principle to deduce the existence of solution. The emphasis here is that f depends on higher order derivatives. Two examples are also included to dwell upon the importance of the results obtained.

Lidstone boundary value problem， Maximum principle， Lower and upper solutions

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2005年01月26日

【期刊论文】Periodic solutions for a kind of second order differential equation with multiple deviating arguments☆

葛渭高， Shiping Lu a， *， Weigao Ge b

Applied Mathematics and Computation 146(2003)195-209，-0001，（）：

-1年11月30日

摘要

By means of continuation theorem of coincidence degree theory, some new results on the existence, and nonexistence of periodic solutions for a kind of second order functional differential equation with multiple deviating arguments are obtained.

Periodic solution， Continuation theorem， Deviating argument

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