Existence and uniqueness of the solutions of nonlinear \(n\)-point boundary value problem. (English) Zbl 0810.34014

Sheng, Qin; Agarwal, Ravi P.

Nonlinear World 2, No. 1, 69-86 (1995).

Summary: We establish the existence and uniqueness of the solutions of first-order nonlinear \(n\)-point boundary value problems by means of the variation of parameter methods. The established theorems correct mistakes in some recent papers and extend the known results in nonlinear variation of parameter methods.

MSC:

34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems, general theory

Keywords:

existence; uniqueness; first-order nonlinear \(n\)-point boundary value problems; nonlinear variation of parameter methods