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Linear distributional differential equations of the second order

Milan Tvrdý (1994)

Mathematica Bohemica

The paper deals with the linear differential equation (0.1) ( p u ' ) ' + q ' u = f ' ' with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).

Linearisation of second-order differential equations.

Eduardo Martínez (1996)

Extracta Mathematicae

Given a second order differential equation on a manifold we find necessary and sufficient conditions for the existence of a coordinate system in which the system is linear. The main tool to be used is a linear connection defined by the system of differential equations.

Linearization techniques for See PDF -control problems and dynamic programming principles in classical and See PDF -control problems

Dan Goreac, Oana-Silvia Serea (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of the paper is to provide a linearization approach to the See PDF -control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating See PDF problems in continuous and lower semicontinuous setting.

Linearization techniques for 𝕃 ∞ See PDF-control problems and dynamic programming principles in classical and 𝕃 ∞ See PDF-control problems

Dan Goreac, Oana-Silvia Serea (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of the paper is to provide a linearization approach to the 𝕃 ∞ See PDF-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the 𝕃 p See PDF approach and the associated linear formulations. This seems to be the most appropriate tool for treating 𝕃 ∞ See PDF problems in continuous and lower semicontinuous...

Local Lipschitz continuity of the stop operator

Wolfgang Desch (1998)

Applications of Mathematics

On a closed convex set Z in ℝ N with sufficiently smooth ( 𝒲 2 , ∞ ) boundary, the stop operator is locally Lipschitz continuous from 𝐖 1 , 1 ( [ 0 , T ] , ℝ N ) × Z into 𝐖 1 , 1 ( [ 0 , T ] , ℝ N ) . The smoothness of the boundary is essential: A counterexample shows that 𝒞 1 -smoothness is not sufficient.

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