Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results
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https://doi.org/10.12775/TMNA.2015.022Słowa kluczowe
Fractional differential equations, semilinear equations, comparison results, critical nonlinearitiesAbstrakt
In this work we study several questions concerning to abstract fractional Cauchy problems of order $\alpha\in(0,1)$. 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.Pobrania
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2015-06-01
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CARVALHO, Alexandre Nolasco, CARVALHO-NETO, Paulo M. Carvalho-Neto, MARÍN-RUBIO, Pedro & ANDRADE, Bruno de. Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2015, T. 45, nr 2, s. 439–467. [udostępniono 22.7.2024]. DOI 10.12775/TMNA.2015.022.
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