Agarwal, S.; Bahuguna, D. Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions. (English) Zbl 1122.34344 Int. J. Math. Math. Sci. 2004, No. 37-40, 1943-1956 (2004). The authors investigate nonlinear retarded differential equations in a real Hilbert space \(H\) of the form \[ u'(t)+A(u(t))=f(t,u(t),u(r_1(t)),\ldots,u(r_m(t))),\quad t\in(0,T], \]\[ h(u_{[-\tau,0]})=\phi_0, \] where \(\phi_0\in C([-\tau,0],H)\) and \(A\) is a single valued maximal monotone operator. The authors show under suitable Lipschitz conditions on \(f\) and surjectivity type conditions on \(h\) the existence of a maximal solution. Further, they estimate the rate of convergence for certain time-discretization schemes. Reviewer: Andras Batkai (Roma) Cited in 7 Documents MSC: 34K30 Functional-differential equations in abstract spaces 47H06 Nonlinear accretive operators, dissipative operators, etc. Keywords:nonlinear retarded equations; time discretizations PDFBibTeX XMLCite \textit{S. Agarwal} and \textit{D. Bahuguna}, Int. J. Math. Math. Sci. 2004, No. 37--40, 1943--1956 (2004; Zbl 1122.34344) Full Text: DOI EuDML