Displaying similar documents to “Comparison theorems for a class of first order Hamilton-Jacobi equations”

Singular Dirichlet boundary value problems. II: Resonance case

Donal O'Regan (1998)

Czechoslovak Mathematical Journal

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Existence results are established for the resonant problem y ' ' + λ m a y = f ( t , y ) a.e. on [ 0 , 1 ] with y satisfying Dirichlet boundary conditions. The problem is singular since f is a Carathéodory function, a ∈ L l o c 1 ( 0 , 1 ) with a > 0 a.e. on [ 0 , 1 ] and ∫ 0 1 x ( 1 - x ) a ( x ) d x < ∞ .

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness...

How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: inf ( u , v ) ∈ 𝒰 a d ∫ 0 1 f t , u ( θ v ( t ) ) , u ' ( t ) , v ( t ) d t , (1) where 𝒰 a d is a set of admissible controls and θ v is the solution of the following equation: { d θ ( t ) d t = g ( t , θ ( t ) , v ( t ) ) , t ∈ [ 0 , 1 ] ; θ ( 0 ) = θ 0 , θ ( t ) ∈ [ 0 , 1 ] ∀ t . (2). The results are nonlocal and new.

Critical diffusions

Edward Nelson (1985)

Séminaire de probabilités de Strasbourg

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