On an Abstract Integral Equation
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The existence of solutions of the nonlinear Volterra equation \[u(t) + \int_0^t {k(t - s)} gu(s)ds \ni f(t)\] is studied in a real Hilbert space. The nonlinear operator g is assumed to be the subdifferential of a convex function. The results obtained extend earlier ones by Barbu (SIAM J. Math. Anal., 1975), Londen (SIAM J. Math. Anal., 1977) and Londen and Staffans (Proc. Amer. Math. Soc., 1978).
Other nonlinear integral equations, Volterra integral equations, existence of solutions, Hilbert space, Abstract integral equations, integral equations in abstract spaces, nonlinear Volterra equation, maximal monotone operators, Monotone operators and generalizations, uniqueness of solutions, abstract integral equation
Other nonlinear integral equations, Volterra integral equations, existence of solutions, Hilbert space, Abstract integral equations, integral equations in abstract spaces, nonlinear Volterra equation, maximal monotone operators, Monotone operators and generalizations, uniqueness of solutions, abstract integral equation
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