Electron. J. Diff. Eqns., Vol. 2008(2008), No. 154, pp. 1-15.

Asymptotic conditions for solving non-symmetric problems of third order nonlinear differential systems

Awar Simon Ukpera

This article presents asymptotic conditions, under various sharp and nonuniform nonresonance assumptions, for solving the forced third order nonlinear system $X''' + A X'' + BX' + sH(t,X) = P(t)$, in which $A$, $B$ and other associated matrices are not necessarily symmetric. This work generalizes some results in the literature which are hinged basically on symmetry considerations.

Submitted November 24, 2006. Published November 7, 2008.
Math Subject Classifications: 34B15, 34C15, 34C25.
Key Words: Asymptotic conditions; third order nonlinear differential systems; non-symmetric problems; sharp and nonuniform nonresonance.

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Awar Simon Ukpera
Department of Mathematics
Obafemi Awolowo University
Ile-Ife, Nigeria
email: aukpera@oauife.edu.ng

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