Abstract :
Following from the proof of spectrum theory of completely continuous linear
operators, we give an abstract result concerning the estimates of norms of positively
homogeneous operators in this paper. Using this result and some duality
theorems for coincidence degree due to A. Capietto, J. Mawhin, and F. Zanolin
Trans. Amer. Math. Soc. 329, 1992, 41]72., the periodic boundary value problem
of asymptotically positively homogeneous differential equations will be studied and
the present results sharply improve those obtained earlier
