Milan Tvrdý

Construction of lower and upper functions and their application to regular and singular periodic boundary value problems

We present new existence and multiplicity results for regular and singular periodic second order boundary value problems

A TOPOLOGICAL APPROACH TO PERIODIC OSCILLATIONS RELATED TO THE LIEBAU PHENOMENON

Abstract We give some sufficient conditions for existence, non-existence and localization of positive solutions for a periodic boundary value problem related to the Liebau phenomenon. Our approach is of topological nature and relies on the Krasnoselskiĭ–Guo theorem on cone expansion and compression. Our results improve and complement earlier ones in the literature.

Nonmonotone impulse effects in second-order periodic boundary value problems

We deal with the nonlinear impulsive periodic boundary value problem u″=f(t,u,u′), u(ti

METHOD OF LOWER AND UPPER FUNCTIONS IN IMPULSIVE PERIODIC BOUNDARY VALUE PROBLEMS

We present here new existence results for the nonlinear second order impulsive periodic boundary value problem. They rely on the presence of a pair of associated lower/upper functions. In contrast to the results known up to now, we need not assume that they are well-ordered.

New results for the Liebau phenomenon via fixed point index

Abstract We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature.