Opuscula Math. 31, no. 3 (2011), 443-455
On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces
Abstract. In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.
Keywords: integrodifferential equations, nonlocal initial condition, completely continuous operator, Schaefer fixed point theorem, mild solutions.
Mathematics Subject Classification: 34G20.