Name: A Note on a Boundary Value Problem
Creator: Lian-Xi Ku
Keywords: Nonlinear boundary value problems for ordinary differential equations, Robin's boundary value problem, existence

A note on a boundary value problem

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 2000Publisher:Springer Science and Business Media LLCJournal:Southeast Asian Bulletin of Mathematics, volume 24, pages 375-382 (issn: 0129-2021,

Authors: Lian-Xi Ku;

doi: 10.1007/s100120050004 , 10.1007/s10012-000-0375-0

A Note on a Boundary Value Problem

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Abstract

Consider Robin's boundary value problem \[ x''=f(t,x,x'),\quad a_0 x(0)-a_1 x'(0)=A,\quad b_0 x(1)-b_1 x'(1)=B, \] where \( A,B \) are arbitrary real numbers, and \(a_0, a_1, b_0, b_1 \) are nonnegative real constants. The author derives conditions on the function \(f\) and its derivatives under which there exists a unique solution to this problem.

Keywords

Nonlinear boundary value problems for ordinary differential equations, Robin's boundary value problem, existence

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