Abstract
AbstractExistence results for a Cauchy problem driven by a semilinear differential Sturm-Liouville inclusion are achived by proving, in a preliminary way, an existence theorem for a suitable integral inclusion. In order to obtain this proposition we use a recent fixed point theorem that allows us to work with the weak topology and the De Blasi measure of weak noncompactness. So we avoid requests of compactness on the multivalued terms. Then, by requiring different properties on the map p involved in the Sturm-Liouville inclusion, we are able to establish the existence of both mild solutions and strong ones for the problem examinated. Moreover we focus our attention on the study of controllability for a Cauchy problem governed by a suitable Sturm-Liouville equation. Finally we precise that our results are able to study problems involving a more general version of a semilinear differential Sturm-Liouville inclusion.
Funder
Università degli Studi di Perugia
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Analysis
Reference34 articles.
1. Berry, M.V.: Stable and unstable Airy-related caustics and beams. J. Opt. 19 (2017). https://doi.org/10.1088/2040-8986/aa6281
2. Bonanno, G., Iannizzotto, A., Marras, M.: On ordinary differential inclusions with mixed boundary conditions. Differ. Integral Equ. 30, 273–288 (2017)
3. Bonanno, G., Iannizzotto, A., Marras, M.: Two positive solutions for superlinear Neumann problems with a complete Sturm-Liouville operator. J. Convex Anal. 25, 421–434 (2018)
4. Cardinali, T., Continelli, E.: Existence results for implicit nonlinear second order differential inclusions. Mediterr. J. Math. 20, 20 (2023). https://doi.org/10.1007/s00009-022-02249-2
5. Cardinali, T., Continelli, E.: Sturm-Liouville differential inclusions with set-valued reaction term depending on a parameter. Results Math. 78, 80 (2023). https://doi.org/10.1007/s00025-023-01857-y