Existence for nonlinear functional differential equations
Two local existence results are obtained for strongly nonlinear functional differential equations of the form \(du/dt(t)+Au(t)\ni F(t,u_ t),\) \(0\leq t\leq T\), \(u(s)=g(s)\), -r\(\leq s\leq 0\). With X a real Banach space, A: D(A)\(\subset X\to 2\) X a m-accretive operator, possibly nonlinear and multivalued, U a nonempty subset in C([-r,0];X), F: [0,T]\(\times U\to X\) is a given mapping and \(g\in U\) satisfies g(0)\(\in D(A)\). The results require certain compactness properties on the operator A. Examples illustrate the applicability of the theory.
strongly nonlinear functional differential equations
scientific article; zbMATH DE number 4069381