In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivia...In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.展开更多
The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presente...The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presented. The special case when φ(s) = |s|p-2 s,p > 1 is also considered. Our analysis is based on the nonlinear alternative of Leray-Schauder and barrier strips.展开更多
基金This work was supported by Key Academic Discipline of Zhejiang Province of China(2005)the Natural Science Foundation of Zhejiang Province of China(Y605144)the Education Department of Zhejiang Province of China(20051897).
文摘In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.
基金the National Science Function of China (19971037)
文摘The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presented. The special case when φ(s) = |s|p-2 s,p > 1 is also considered. Our analysis is based on the nonlinear alternative of Leray-Schauder and barrier strips.
