Method of successive approximations for a certain non-linear third order boundary value problem. (English) Zbl 0707.34019

Rusnák, Ján

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 88, Math. 26, 161-168 (1987).

A method of successive approximations formed by means of lower and upper solutions is applied to a monotone operator based on Green’s functions and used to investigate a boundary value problem of the form \[ x'''=f(t,x,x'),\quad \alpha_ 2x'(a_ 1)-\alpha_ 3x''(a_ 1)=A_ 1,\quad x(a_ 2)=A_ 2,\quad \gamma_ 2x'(a_ 3)+\gamma_ 3x''(a_ 3)=A_ 3, \] under suitable sign restrictions upon the \(\alpha_ i\), the condition \(a_ 1<a_ 2<a_ 3\) and some monotonicity conditions upon f.

Reviewer: J.Mawhin

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

lower solution; method of successive approximations; upper solutions; Green’s functions

References:

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