Existence theorems for lagrange control problems with unbounded time domain

Existence Theorems for General Control Problems of Bolza and Lagrange

The existence of solutions is established for a very general class of problems in the calculus of variations and optimal control involving ordinary differential equations or contingent equations. The theorems, while relatively simple to state, cover, besides the more classical cases, problems with considerably weaker assumptions of continuity or boundedness. For example, the cost functional may...

Existence Theorems for Multidimensional Lagrange Problemsl

Existence theorems are proved for multidimensional Lagrange problems of the calculus of variations and optimal control. The unknowns are functions of several independent variables in a fixed bounded domain, the cost functional is a multiple integral, and the side conditions are partial differential equations, not necessarily linear, with assigned boundary conditions. Also, unilateral constraint...

EXISTENCE OF A STEADY FLOW WITH A BOUNDED VORTEX IN AN UNBOUNDED DOMAIN

We prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. The data prescribed is the rearrangement class of the vorticity field. The corresponding stream function satisfies a semilinear elliptic partial differential equation. The result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

Uniqueness Theorems for Multidimensional inverse Problems with Unbounded Coefficients

Existence Theorems for Generalized Nash Equilibrium Problems

In a recent paper [7], Dutang provided a thorough study of theorems guaranteeing existence of generalized Nash equilibria and analyze the assumptions on practical parametric feasible sets. Motivated by [7], firstly in this paper, we obtain a generalization (Theorem 1) of an equilibrium theorem for a competitive economy due to Arrow and Debreu [1]. Secondly, we show that our previous generalizat...