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Volterra integral equations associated with a class of nonlinear operators in Hilbert spaces. (English) Zbl 0608.45008
Let H be a real Hilbert space. We study the nonlinear Volterra equation \[ u(t)+\int ^{t}_{0}b(t-s)Au(s)ds\ni F(t),\quad 0\leq t\leq T \] where b and F are respectively a scalar and a vector valued function and A is a (possibly multivalued) operator not necessarily monotone, namely a (\(\phi\),f)-monotone operator. Under suitable hypotheses we prove various existence, uniqueness and regularity results for the solution u. Some examples which illustrate the abstract results are presented.

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
47H05 Monotone operators and generalizations
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