Nonautonomous locally Lipschitz continuous functional differential equations in spaces of continuous functions

Journal article

A local existence and uniqueness result for the functional differential equation in a Banach space X x′(t) ∈ f(t)x(t) + g(t)xt, 0 ≤ t ≤ T, (FDE) x0 = φ ∈ C(-R, 0; X) is obtained, for the case where the operators f(t) satisfy only a local dissipativity condition and the operators g(t) are only locally Lipschitz continuous. The conditions include equations defined on cones.

Authors: Dyson, J; Villella Bressan, R

• Publication status: Published
• Journal: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
• Volume: 3
• Issue: 1
• Pages: 127-147
• Publication date: 1996-03-01
• DOI: 10.1007/BF01194220
• EISSN: 1420-9004
• ISSN: 1021-9722
• Language: English