Existence and regularity results for an integral equation with infinite delay in a Banach space

Some integrodifferential equations with infinite delay in Banach spaces are studied.

[1]  P. Clément.  On abstract Volterra equations in Banach spaces with completely positive kernels , 1984 .

[2]  A. Lunardi.  Interpolation Spaces Between Domains of Elliptic Operators and Spaces of Continuous Functions with Applications to Nonlinear Parabolic Equations , 1985 .

[3]  J. J. Levin.  Resolvents and bounds for linear and nonlinear Volterra equations , 1977 .

[4]  J. Nohel,et al.  Abstract Linear and Nonlinear Volterra Equations Preserving Positivity , 1979 .

[5]  G. Prato,et al.  Periodic solutions for linear integrodifferential equations with infinite delay in Banach spaces , 1986 .

[6]  Jan Prüss,et al.  Bounded solutions of Volterra equations , 1988 .

[7]  R. MacCamy.  Stability Theorems for a Class of Functional Differential Equations , 1976 .

[8]  Eugenio Sinestrari,et al.  On the abstract Cauchy problem of parabolic type in spaces of continuous functions , 1985 .

[9]  G. Gripenberg.  On the resolvents of Volterra equations with nonincreasing kernels , 1980 .

[10]  G. Prato,et al.  Solvability on the real line of a class of linear volterra integrodifferential equations of parabolic type , 1988 .

[11]  On a nonlinear Volterra equation , 1972 .

[12]  H. Stewart.  Generation of analytic semigroups by strongly elliptic operators , 1974 .

[13]  Paul L. Butzer,et al.  Semi-groups of operators and approximation , 1967 .

[14]  Jace W. Nunziato,et al.  On heat conduction in materials with memory , 1971 .

[15]  Yoshio Yamada,et al.  Bifurcation of periodic solutions for nonlinear parabolic equations with infinite delays , 1986 .

[16]  J. Nohel,et al.  Asymptotic Behavior of Solutions of Nonlinear Volterra Equations with Completely Positive Kernels , 1981 .