Singularity diferenciální rovnice
Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.
Nous considérons les équations différentielles possédant un paramètre de contrôle, singulièrement perturbées par un petit paramètre . Nous prouvons alors, par des techniques de majoration directe, que les solutions formelles et le paramètre de contrôle sont des séries Gevrey en .
We give some results about the topological structure of solution sets of multivalued Sturm-Liouville problems in Banach spaces.