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):
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.
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