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18<br />

First-Order Three-Point Boundary Value Problems at<br />

Resonance<br />

Mesliza Mohamed<br />

email: mesliza@perlis.uitm.edu.my<br />

Jabatan Matematik, Universiti Teknologi MARA, Kampus Arau 02600 Arau, Perlis<br />

Malaysia<br />

(Joint work with: H.B. Thompson, M. Jusoh)<br />

Abstract: We consider three-point boundary value problems for a system of first-order<br />

equations in perturbed systems of ordinary differential equations at resonance. We obtain<br />

new results for the above boundary value problems with nonlinear boundary conditions.<br />

In particular, we consider a system of first-order equations which is arising from scalar<br />

second-order equation. The existence of solutions is established by applying a version of<br />

Brouwer’s Fixed Point Theorem which is due to Miranda.

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