On a class of doubly nonlinear nonlocal evolution equations

摘要

This note deals with the initial value problem for the abstract nonlinear nonlocal equation (Au)' + (Bu) f, where A is a possibly degenerate maximal monotone operator from the Hilbert space V to its dual space V~*, while B is a nonlocal maximal monotone operator from L~2(0, T, V) to L~2(0, T; V~*). Assuming suitable boundedness and coerciveness conditions and letting A be a subgradient, existence of a solution is established by making use of an approximation procedure. Applications to various classes of degenerate nonlinear integrodifferential equations are discussed.