Special modes in a two-sector economy model with an integral utility function

In this work, we study a two-sector economic model with the Cobb–Douglas production function on an infinite planning horizon where the utility function is a functional of an integral form and a Lagrangian of a logarithmic type. A one-dimensional equation is obtained that depends only on the coefficients of elasticity and amortization, and determines the possible special modes. The special modes are described in analytical form.