Blow-up and global existence of solutions to integral equations with infinite delay in Banach spaces. (English) Zbl 1238.45009

Xiao, Ti-Jun; Liang, Jin

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e1442-e1447 (2009).

Summary: We present new blow-up theorems, which are only in terms of the ordinary limit, for the solutions to the Cauchy problem for integral equations with infinite delay in Banach spaces. Moreover, we provide an example to illustrate our abstract result.

MSC:

45N05	Abstract integral equations, integral equations in abstract spaces
47N20	Applications of operator theory to differential and integral equations

Keywords:

Cauchy problem; integral equation; infinite delay; blow-up; Banach space

References:

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