MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 587-595, 2014

Functional-differential equations with Riemann-Liouville integrals in the nonlinearities

Milan Medveď

Milan Medveď, Comenius University in Bratislava, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, Mlynsk√° dolina, 842 48 Bratislava, Slovak Republic, e-mail: Milan.Medved@fmph.uniba.sk

Abstract: A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels. The result is illustrated on an example of a scalar equation with one Riemann-Liouville integral.

Keywords: fractional differential equation; Riemann-Liouville integral; blowing-up solution

Classification (MSC 2010): 34K37, 34A08, 34K05, 34G20


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