Positive solutions for boundary-value problems of nonlinear fractional differential equations.
We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.
Si prova che ogni polinomio in una variabile reale di grado è somma di funzioni periodiche, ovviamente non tutte continue, e che ci sono funzioni di una variabile reale che non sono somma di un numero finito di funzioni periodiche.
In the first part of this paper we establish the theory of rapid variation on time scales, which corresponds to existing theory from continuous and discrete cases. We introduce two definitions of rapid variation on time scales. We will study their properties and then show the relation between them. In the second part of this paper, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. Note...