Evolution inclusions involving a difference term of subdifferentials and applications
This paper considers the following differential inclusion \[ -x'(t)\in\partial\phi_1(x(t))- \partial\phi_2(x(t))- F(t,x(t))\tag{1} \] in a Hilbert space. Here \(\phi_1\) and \(\phi_2\) are lower semicontinuous, convex functions, \(\partial\) denotes subdifferential, and \(F(t,x)\) is a set-valued function. Existence theorems under various assumptions on \(F\) (upper or lower semicontinuity) are proved together with a bang-bang theorem. Some examples illustrating applicability of the above results are given.
scientific article; zbMATH DE number 1062330