A remark on singular perturbation methods (Q1070097)

The author improves a result of \textit{P. C. Fife} [J. Math. Anal. Appl. 54, 497-521 (1976; Zbl 0345.34044)] on the existence and asymptotic behavior of solutions of the singularly perturbed system \(\epsilon^ 2u''=f(u,v),\quad v''=g(u,v),\) where u(0), u(1), v(0) and v(1) are prescribed, by removing a boundedness condition on the partial derivative \(g_ u\).