Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 154, pp. 1-15.

Title: Asymptotic conditions for solving non-symmetric problems
       of third order nonlinear differential systems
   
Author: Awar Simon Ukpera (Obafemi Awolowo Univ., Nigeria)

Abstract:
 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 07, 2008.
Math Subject Classifications: 34B15, 34C15, 34C25.
Key Words: Asymptotic conditions;
 third order nonlinear differential systems; 
 non-symmetric problems; sharp and nonuniform nonresonance.