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

Medveď, Milan

Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 587-595

Abstract (VO)

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.

Détail

DOI : 10.21136/MB.2014.144136

Classification : 34A08, 34G20, 34K05, 34K37
Keywords: fractional differential equation; Riemann-Liouville integral; blowing-up solution

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