非线性三阶三点边值问题系统正解的存在性及多解性

发布时间：2018-05-23 22:06

  本文选题：系统 + 边值问题　； 参考：《兰州理工大学》2017年硕士论文

【摘要】：三阶微分方程在我们的生活中有着非常广泛的应用,其中涉及到了应用数学和物理学的各种不同领域,例如,地球引力吹积的涨潮、三层梁、带有固定或变化横截面的屈曲梁的挠度、电磁波等.因而,更多的学者关注于三阶微分方程多点边值问题的研究,并获得了非常丰富的研究结果.伴随着人们更深入的研究与探讨三阶微分方程多点边值问题,三阶微分方程多点边值问题系统也慢慢成为人们所热衷研究的对象.本文讨论了下述非线性三阶三点微分方程边值问题系统正解的存在性及多解性,其中0η≤?,0≤α1,f,g∈C([0,1]×[0,∞),[0,∞)),并且对于所有的t∈[0,1],都有f(t,0)≡0,g(t,0)≡0.所用的工具是不动点指数理论.
[Abstract]:Third order differential equations have a very wide range of applications in our lives, involving various fields of applied mathematics and physics, for example, the Earth's gravitational rising tide, the three-story beam, Deflection, electromagnetic waves, etc., of a buckled beam with a fixed or varying cross section. Therefore, more and more scholars pay attention to the multi-point boundary value problem of the third order differential equation, and obtain very rich research results. With the further study and discussion of the multipoint boundary value problem of the third order differential equation, the system of the multipoint boundary value problem of the third order differential equation has gradually become the object that people are keen to study. In this paper, we discuss the existence and multiplicity of positive solutions of the following nonlinear third-order three-point boundary value problem systems, where 0 畏 鈮，

本文编号：1926557