AN ABSTRACT RESULT ON ASYMPTOTICALLY POSITIVELY HOMOGENEOUS DIFFERENTIAL-EQUATIONS

Following from the proof of spectrum theory of completely continuous l inear operators, we give an abstract result concerning the estimates o f norms of positively homogeneous operators in this paper. Using this result and some duality theorems for coincidence degree due to A. Capi etto, J. Mawhin, and F. Zanolin (Trans. Amer. Math. Sec. 329, 1992, 41 -72), the periodic boundary value problem of asymptotically positively homogeneous differential equations will be studied and the present re sults sharply improve those obtained earlier. (C) 1997 Academic Press.