Exactsolutionsofsomelineardifferentialequationsandpositivesolutionsofthecorrespondingnonlinearequations资源-CSDN文库

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˖ڍመ᝶஠ڙጲ

http://www.paper.edu.cn

某些线性微分方程的解析解和相应非线性方

程的正解

赵增勤

曲阜师范大学数学科学学院，曲阜 273165

摘要：对于某些具有泛函边界条件的线性微分方程，通过格林函数给出了解的解析表达式. 利

用得到的格林函数，研究了具有可数多个点的非局部边界条件和积分边界条件下的相应超线性

方程正解的存在性.

关键词：应用数学；解析解；线性泛函边界条件；格林函数；正解

中图分类号： O175.14

Exact solutions of some linear diﬀerential

equations and positive solutions of the

corresponding nonlinear equations

ZHAO Zengqin

School of Mathematical Sciences, Qufu Normal University, Qufu 273165

Abstract: Exact expressions of the solutions for some linear diﬀerential equations with

functional boundary conditions are given by the Green’s functions. Using Green’s functions

obtained we investigate existence of positive solutions for the corresponding superlinear

equations with countably many points and integral boundary conditions.

Key words: Applied mathematics; Exact solution; linear functional boundary condition;

Green’s function; positive solution.

0 Introduction and the main results

The theory of non-local boundary value problems has been emerging as an important

area of investigations in recent years. The investigation of equation u

+ f(t, u) = 0 with

non-local boundary conditions (multi-point or integral boundary conditions) can be seen in

[1, 2, 3, 4, 5, 6, 7, 8] and its references. The investigation of one-dimensional p-Laplacian non-

local boundary problems can be seen in [9, 10, 11, 12] and its references. But conclusions of

基金项目： Research supported by the National Natural Science Foundation of China (11571197)，and the

Doctoral Program Foundation of Education Ministry of China (20133705110003)

作者简介： Zhao Zengqin (1955-), male，professor，major research direction：Nonlinear functional analysis and

its application.

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Exact solutions of some linear differential equationsand positiv...