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Zbl 1227.35239
Arara, A.; Karande, B.D.; Benchohra, M.; Dhage, B.C.
Existence theorems for a class of hyperbolic integro-differential equations in Banach algebras. (English)
[J] J. Nat. Phys. Sci. 20, No. 1-2, 51-63 (2006). ISSN 0970-3799

Summary: Some results concerning the existence as well as existence of extremal solutions are proved for hyperbolic quadratic integro-differential equations using a nonlinear alternative of Leray-Schauder type and using a hybrid fixed point theorem on ordered Banach algebras due to {\it B. C. Dhage} [Kyungpook Math. J. 45, No.~2, 281--292 (2005; Zbl 1092.47047); Panam. Math. J. 9, No.~4, 83--102 (1999; Zbl 0964.47026)].

MSC 2000:: *35R09
35L70 Second order nonlinear hyperbolic equations
35L20 Second order hyperbolic equations, boundary value problems

Keywords: hyperbolic integro-differential equation; existence theorem; Banach algebras

Citations: Zbl 1092.47047; Zbl 0964.47026

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