A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.
The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characteriza- tions such that every half-space in Banach space X and every weak^＊ half-space in the dual space X^＊ are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.
