Electron. J. Diff. Equ., Vol. 2013 (2013), No. 18, pp. 1-13.

Existence of solutions for nonlinear impulsive neutral integro-differential equations of Sobolev type with nonlocal conditions in Banach spaces

Bheeman Radhakrishnan, Aruchamy Mohanraj, Velu Vinoba

In this article, we prove the existence of mild and strong solutions for nonlinear impulsive integro-differential equations of Sobolev type with nonlocal initial conditions. The results are obtained by using semigroup theory and the Schauder fixed point theorem. An example is provided to illustrate the theory.

Submitted September 6, 2012. Published January 21, 2013.
Math Subject Classifications: 34A37, 47D06, 47H10, 74H20, 34K40.
Key Words: Existence; neutral differential equation; fixed point theorem; impulsive differential equation.

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Bheeman Radhakrishnan
Department of Applied Mathematics and Computational Sciences
PSG College of Technology
Coimbatore - 641 004, TamilNadu, India
email: radhakrishnanb1985@gmail.com
Aruchamy Mohanraj
Department of Mathematics and Computer Sciences
SVS College of Engineering
Coimbatore - 642 109, TamilNadu, India
email: mohanraj.mat@gmail.com
Velu Vinoba
Department of Mathematics
K. N. Govt. Arts College for Women
Thanjavur, TamilNadu, India
email: vinoba2012@gmail.com

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