On the existence of solutions for the abstract differential equations of Sobolev type (Q2766299)

The authors consider the following Cauchy problem for an abstract differential equation of Sobolev type: \(Bu''(t)+ Au(t) \ni f(t)\), a.e. on \([0,T]\), \(u(0)=u_0, B^{\frac{1}{2}}u'(0)= B^{\frac{1}{2}}u_1\), in a real Hilbert space \(H\). Here, \(A\) is a nonlinear maximal monotone operator in \(H\), and \(B\) is a nonnegative selfadjoint operator in \(H\). The authors establish the existence and uniqueness of strong solutions, and they give an application of their result in the study of some nonlinear partial differential equations.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00042].