Open Access Open Access  Restricted Access Subscription or Fee Access

Nonlocal Semi-linear Hyperbolic Integro-differential Equations in a Banach Space

D. Bahuguna, D.N. Pandey, A. Ujlayan

Abstract


In this paper we consider an abstract nonlocal semi-linear hyperbolic integro-differential equation in a Banach space. Using the theory of strongly continuous semigroups, we establish the existence and uniqueness of a mild solution, under certain Lipschitz conditions on the nonlinear maps and an integrability condition on the kernel. The existence of a classical solution of the problem considered is proved under some additional conditions on the nonlinear maps.

Keywords


Hyperbolic integro-differential equation, nonlocal Cauchy problem, mild solution, classical solution.

Full Text:

PDF

Refbacks

  • There are currently no refbacks.


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.