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IMCS/Publications/BASM/Issues/BASM n.2 (66), 2011/

The Variational Approach to Nonlinear Evolution Equations

Authors: Viorel Barbu

Abstract

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):VV′ 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.

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