EXISTENCE AND UNIQUENESS OF MILD AND STRONG SOLUTIONS OF A VOLTERRA INTERGRODIFFERENTIAL EQUATION WITH NONLOCAL CONDITIONS

Authors

  • K. BALACHANDRAN Department of Mathematics • Bharathiar University, Coimbatore-641 046 ** CBM College, Coimbatore:.641042 Tamil Nadu, India.
  • S. ILAMARAN Department of Mathematics • Bharathiar University, Coimbatore-641 046 ** CBM College, Coimbatore:.641042 Tamil Nadu, India.

DOI:

https://doi.org/10.5556/j.tkjm.28.1997.4323

Keywords:

Existence of solutions, Volterra intcgrodiffercntial equation, nonlocal condition, semigroup of operators

Abstract

We prove the existence and uniqueness of mild and strong solutions of a Volterra integrodifferential equation with nonlocal initial conditions using the method of semigroups and the Banach fixed point theorem.

References

K. Balachandran and S. Ilamaran, "Existence and uniqueness of mild and strong solutions of a semilinear evolution equation with nonlocal condition," Indian J. Pure and Appl. Math 25 (1994), 411-418.

L. Byszewski, "Theorems about the existence and uniqueness of solutions of a semilincar evolution nonlocal Cauchy problem," J. Math. Anal. and Appl., 162. 2 (1991), 494-505.

C. Corduneanu, "Integral Equations and Applications," Cambridge University Press, 1991

G. Gripenberg, S. O. Londen, O. Staffens, "Volterra Integral and Functional Equations," Cambridge University Press, 1990.

A. Pazy, "Semigroups of Linear Operators and Applications to Partial differential equa­tions," Springer-Verlag, NewYork, 1983.

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Published

1997-06-01

How to Cite

BALACHANDRAN, K., & ILAMARAN, S. (1997). EXISTENCE AND UNIQUENESS OF MILD AND STRONG SOLUTIONS OF A VOLTERRA INTERGRODIFFERENTIAL EQUATION WITH NONLOCAL CONDITIONS. Tamkang Journal of Mathematics, 28(2), 93-100. https://doi.org/10.5556/j.tkjm.28.1997.4323

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Papers