MMN-2407

Multiple solutions of a Dirichlet problem in one-dimensional billiard space

Jan Tomecek;

Abstract

The paper gives multiplicity results for an impulsive boundary value problem. This problem can be understood as a problem in one-dimensional billiard space and it is also a generalization of oscillator with obstacles from below and from above and absolutely elastic impacts. A simple condition for the existence of solution with exact number of impacts is given, as well as the multiplicity result. The results are obtained by a transformation into problem without impulses (without impacts) and using Schauder fixed point theorem.


Vol. 20 (2019), No. 2, pp. 1261-1272
DOI: https://doi.org/10.18514/MMN.2019.2407


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