一类三阶常微分方程非线性三点边值问题解的存在性

In this paper, existence of solutions of third-order differential equation
y′″（t）=f（t,y（t）,y′（t）,y″（t））
with nonlinear three-point boundary condition
{g（y（a）,y′（a）,y″（a））=0,
h（y（b）,y′（b））=0,
I（y（c）,y′（c）,y″（c））=0
is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f ： [a,c]×R^3→R,g：R^3→R,h：R^2→R and I：R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper.

Existence of Solutions of a Nonlinear Three-Point Boundary Value Problem for Third-Order Ordinary Differential Equations

In this paper, existence of solutions of third-order differential equation $$y'(t)=f(t,y(t),y'(t),y'(t))$$ with nonlinear three-point boundary condition $$left{ begin{array}{l} g(y(a),y'(a),y'(a))=0,h(y(b),y'(b))=0,I(y(c),y'(c),y'(c))=0end{array}right.$$is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method, where $a, b, cin R, a