Electron. J. Diff. Eqns., Vol. 2006(2006), No. 80, pp. 1-8.

On the solvability of nonlinear first-order boundary-value problems

Christopher C. Tisdell

This article investigates the existence of solutions to first-order nonlinear boundary-value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point methods.

Submitted April 7, 2006. Published Juy 19, 2006.
Math Subject Classifications: 34B15, 34B99.
Key Words: Existence of solutions; boundary value problems; differential equations; fixed-point methods; differential inequalities.

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Christopher C. Tisdell
School of Mathematics
The University of New South Wales
UNSW Sydney 2052, Australia
email: cct@maths.unsw.edu.au

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