Displaying 1561 – 1580 of 2827

Showing per page

On Semicontinuity in Impulsive Dynamical Systems

Krzysztof Ciesielski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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....

On solutions of differential equations with ``common zero'' at infinity

Árpád Elbert, Jaromír Vosmanský (1997)

Archivum Mathematicum

The zeros c k ( ν ) of the solution z ( t , ν ) of the differential equation z ' ' + q ( t , ν ) z = 0 are investigated when lim t q ( t , ν ) = 1 , | q ( t , ν ) - 1 | d t < and q ( t , ν ) has some monotonicity properties as t . The notion c κ ( ν ) is introduced also for κ real, too. We are particularly interested in solutions z ( t , ν ) which are “close" to the functions sin t , cos t when t is large. We derive a formula for d c κ ( ν ) / d ν and apply the result to Bessel differential equation, where we introduce new pair of linearly independent solutions replacing the usual pair J ν ( t ) , Y ν ( t ) . We show the concavity of c κ ( ν ) for | ν | 1 2 and also...

Currently displaying 1561 – 1580 of 2827