Geodesic
Boundary value problem of Pontryagin's maximum principle in a two-sector economy model with an integral utility function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1812-1826 Cet article a éte moissonné depuis la source Math-Net.Ru

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An infinite-horizon two-sector economy model with a Cobb–Douglas production function and a utility function that is an integral functional with discounting and a logarithmic integrand is investigated. The application of Pontryagin's maximum principle yields a boundary value problem with special conditions at infinity. The search for the solution of the maximum-principle boundary value problem is complicated by singular modes in its optimal solution. In the construction of the solution to the problem, they are described in analytical form. Additionally, a special version of the sweep method in continuous form is proposed, which is of interest from theoretical and computational points of view. An important result is the proof of the optimality of the extremal solution obtained by applying the maximum-principle boundary value problem. 
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Yu. N. Kiselev; M. V. Orlov; S. M. Orlov. Boundary value problem of Pontryagin's maximum principle in a two-sector economy model with an integral utility function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1812-1826. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a1/

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