Asymptotic properties of solutions of time-dependent Volterra integral equations
The author studies the asymptotic behavior as \(t\to \infty\) of solutions of the time-dependent nonlinear Volterra integral equation \[ (1)\quad u(t)+\int^{t}_{0}b(t-s)A(s)u(s)ds\ni f(t),\quad t\in R_+=[0,\infty). \] Here b: \(R_+\to R\) is a given kernel, A(t) is (for each \(t\geq 0)\) a maximal monotone, multivalued operator on a real Hilbert space H and f: \(R_+\to H\). The integral appearing in (1) is taken in the sense of Bochner. The results of the paper generalize a lot of ones concerning (1) when A does not depend on t.
time-dependent nonlinear Volterra integral equation
scientific article; zbMATH DE number 4105586
scientific article