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Semilinear integrodifferential equations with nonlocal initial conditions. (English) Zbl 1068.45014
The paper is concerned with developing existence and uniqueness theorems for the Cauchy problem for semilinear integro-differential equations of convolution type. The sequence of theorems presented extends the existing results and can be applied, as is shown in the final section of the paper, to problems that arise in heat conduction in materials with memory.
MSC:
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations