Existence of local solutions of quasilinear integrodifferential equations in banach spaces

Abstract

We prove the existence and uniquness of local mild arid classical solutions of a quasilinear integrodifferential equation. The results are obtained by using C₀-semigroup and the Banach fixed point theorem.

Keywords:

• C₀ semigroups
• contraction principle
• quasilinear integrodifferential equation

AMS:

• 34G20
• 47H20

^*Permanent Address: Department of Mathematics Bharathiar University Coimbatore-641 046. INDIA.

^*Permanent Address: Department of Mathematics Bharathiar University Coimbatore-641 046. INDIA.

Notes

^*Permanent Address: Department of Mathematics Bharathiar University Coimbatore-641 046. INDIA.