Geodesic
The variational approach to nonlinear evolution equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 89-101

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In this paper, we present a few recent existence results via variational approach for the Cauchy problem $$ \frac{dy}{dt}(t)+A(t)y(t)\ni f(t),\quad y(0)=y_0,\qquad t\in[0,T], $$ where $A(t)\colon V\to V'$ 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. 
@article{BASM_2011_2_a7,
     author = {Viorel Barbu},
     title = {The variational approach to nonlinear evolution equations},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {89--101},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2011_2_a7/}
}
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Viorel Barbu. The variational approach to nonlinear evolution equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 89-101. http://geodesic.mathdoc.fr/item/BASM_2011_2_a7/