奇异三阶三点边值问题解的存在性(英文)

Solvability of Singular Third-Order Three-Point Boundary Value Problems

对于非线性三阶三点边值问题:um(t)=f(t,u(t),u′(t),u″(t))a.e.t∈[0,1],u(0)=a,u′(η) =b,u″(1) =c,建立了一个解的存在定理,其中21≤η<1 .在这个方程中,非线性项f(t,u,v,w)是一个Caratheodoly函数并且边界条件是非齐次的.主要结论是用积分表达的.

An existence theorem of solution is established for the nonlinear third-order three-point boundary value problem um（t）=f（t,u（t）,u′（t）,u″（t））a.e.t∈[0,1],u（0）=a,u′（η） =b,u″（1） =c,where 1/2≤η〈1 .In this problem, the nonlinear term f（ t, u, v, w ） is a Carath6odory function and the boundary condition is nonhomogeneous. Main results are expressed by integral form.