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Existence and uniqueness of solutions for third-order nonlinear boundary value problems. (English) Zbl 1160.34312
Consider the boundary value problem $$y'''f(x,y,y',y''),\ 0<x<1,$$ $$k(y(0),y'(0))=0,\ g(y'(0),y''(0))=0,\tag *$$ $$h(y(0),y'(0),y''(0);\ y(1),y'(1),y''(1))=0,$$ where $k,g$ and $h$ are continuous. The authors provide sufficient conditions for the existence and uniqueness of a solution to (*).

34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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[12] Society, Japanese Mathematical: Encyclopedia of mathematics. (1985)
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