957 research outputs found
Composition principles for generalized almost periodic functions
In this paper, we consider composition principles for generalized almost
periodic functions. We prove several new composition principles for the classes
of (asymptotically) Stepanov -almost periodic functions and (asymptotically,
equi-)Weyl -almost periodic functions, where and explain
how we can use some of them in the qualitative analysis of solutions for
certain classes of abstract semilinear Cauchy inclusions in Banach spaces
Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results
In this work we study several questions concerning to abstract fractional
Cauchy problems of order α ∈ (0, 1). Concretely, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally, by establishing some general comparison results, we apply them to conclude the global well-posedness of a fractional partial differential equation coming from heat conduction theory.Conselho Nacional de Desenvolvimento CientÃfico e TecnológicoCoordenação de aperfeiçoamento de pessoal de nivel superiorFundação de Amparo à Pesquisa do Estado de São PauloMinisterio de EducaciónMinisterio de Ciencia e InnovaciónJunta de AndalucÃ
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