On positive solutions of equations with two middle terms
We investigate the existence of solutions on a compact interval to second order boundary value problems for a class of functional differential inclusions in Banach spaces. We rely on a fixed point theorem for condensing maps due to Martelli.
In the important paper on impulsive systems [K1] several notions are introduced and several properties of these systems are shown. In particular, the function ϕ which describes "the time of reaching impulse points" is considered; this function has many important applications. In [K1] the continuity of this function is investigated. However, contrary to the theorem stated there, the function ϕ need not be continuous under the assumptions given in the theorem. Suitable examples are shown in this paper....
The zeros of the solution of the differential equation are investigated when , and has some monotonicity properties as . The notion is introduced also for real, too. We are particularly interested in solutions which are “close" to the functions , when is large. We derive a formula for and apply the result to Bessel differential equation, where we introduce new pair of linearly independent solutions replacing the usual pair , . We show the concavity of for and also...