The Variational Approach to Nonlinear Evolution Equations
نویسندگان
چکیده
In this paper, we present a few recent existence results via variational approach for the Cauchy problem dy dt (t) + A(t)y(t) ∋ f(t), y(0) = y0, t ∈ [0, T ], where A(t) : V → V ′ is a nonlinear maximal monotone operator of subgradient type in a dual pair (V, V ′) of reflexive Banach spaces. In this case, the above Cauchy problem reduces to a convex optimization problem via Brezis–Ekeland device and this fact has some relevant implications in existence theory of infinite-dimensional stochastic differential equations. Mathematics subject classification: 34H05, 34LRO, 47E05.
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