Some Remarks on the Solvability of Some Abstract Differential Equations
نویسنده
چکیده
This paper is concerned with the solvability of some abstract differential equation of type u̇(t) + Au(t) + Bu(t) ∋ f(t), t ∈ (0, T ], u(0) = 0, where A is a linear selfadjoint operator and B is a nonlinear (possibly multi-valued) maximal monotone operator in a real Hilbert space H with the normalization 0 ∈ B(0). We use the concept of variational sum introduced by H. Attouch, J.-B. Baillon, and M. Théra, to investigate solutions to the given differential equation.
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