Existence and boundedness of solutions of abstract nonlinear integrodifferential equations of nonconvolution type |
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Authors: | Charles Rennolet |
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Institution: | Rose-Hulman Institute of Technology, Terre Haute, Indiana U.S.A. |
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Abstract: | Existence and boundedness theorems are given for solutions of nonlinear integrodifferential equations of type , (1.1) u(0) = u0, Here A and B are nonlinear, possibly multivalued, operators on a Banach space W and a Hilbert space H, where W ? H. The function f (0, ∞) → H and the kernel a(t, s): × → are known functions. The results of this paper extend the results of Crandall, Londen, and Nohel 4] for equation (1.1). They assumed the kernel to be of the type a(t, s) = a(t ? s). We relax this assumption and obtain similar results. Examples of kernels satisfying the conditions we require are given in section 4. |
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