%0 Journal Article
%T 一类三阶周期边值共振问题解的存在性<br>Existence of Solutions for a Class of Third-Order Periodic Boundary Value Problems at Resonance
%A 魏丽萍
%J 四川大学学报 (自然科学版)
%D 2018
%X 本文运用了~Lyapunov-Schmidt~过程和紧向量场方程的解集连通理论为三阶周期边值共振问题 $$ \left\{\begin{array}{ll} v'''(t)=f(t,v(t)),~~\ \ \ t\in [0,T],\\[2ex] v^{(i)}(0)-v^{(i)}(T)=0 ,\ \ \ i=0,1,2 \end{array} \right.\eqno $$ 发展上下解方法,~并且得到其解的存在性结果,~其中函数~$f: [0,T]\times \mathbb{R}\rightarrow \mathbb{{R}}$~连续且有界.<br>By using the Lyapunov-Schmidt procedure and the connectivity theory of the solution set of compact vector fields,~we develope the method of upper and lower solutions and obtain the existence of solutions for a third-order periodic boundary value problem at resonance~ $$ \left\{\begin{array}{ll} v'''(t)=f(t,v(t)),~~\ \ \ t\in [0,T],\\[2ex] v^{(i)}(0)-v^{(i)}(T)=0 ,\ \ \ i=0,1,2, \end{array} \right.\eqno $$ where~$f: [0,T]\times \mathbb{R}\rightarrow \mathbb{R}$~is continuous and bounded
%K Lyapunov-Schmidt~过程 ~连通集 ~无序上下解 ~共振 ~存在性&lt
%K br&gt
%K Lyapunov-Schmidt procedure ~Connected set ~Disordered lower and upper solutions ~Resonance ~ Existence
%U http://science.ijournals.cn/jsunature_cn/ch/reader/view_abstract.aspx?file_no=Z170283&flag=1