ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary We study in this paper the initial value problem for the multivalued differential equation wheref is in MS(2) andG is a multifunction fromC([0, T];Ω) into the closed subsets of L2(0, Y;Ω), satisfying suitable regularity assumptions. As an application we prove a local existence result for the problem $$u\prime (t)2 - \partial ^ - f(u(t)) + G_1 (t,u(t)) + G_2 (t,u(t)),u(0) = u_0 ,$$ , where G1 (resp. G2) is a lower semicontinuous (resp. upper semicontinuous, convex valued) multifunction from [0, T]×Ω into H. No strong compactness is required for the values of G1 and G2. The differential inclusion (*) is also investigated in the case whereG comes from a multivalued regularization of g(t, x, u) and $$\int\limits_0^t {a(} t - s)g(s,;u(s))ds$$ , where g(t, x, u) is a discontinuous real single-valued function defined on [0, T]×Rn×R.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01764124
Permalink
