Necessary Conditions to A Fractional Variational Problem

General necessary conditions for infinite horizon fractional variational problems

We consider infinite horizon fractional variational problems, where the fractional derivative is defined in the sense of Caputo. Necessary optimality conditions for higher-order variational problems and optimal control problems are obtained. Transversality conditions are obtained in the case state functions are free at the initial time.

Necessary Conditions for Solutions to Variational Problems

Ω [F (∇v (x)) + g (x, v (x))] dx with F a convex function defined on RN , it has been conjectured in [2] that the suitable form of the Euler-Lagrange equations satisfied by a solution u should be ∃p(·) ∈ L(Ω), a selection from ∂F (∇u(·)), such that div p(·) = gv(·, u(·)) in the sense of distributions. Equivalently, the condition can be expressed as ∃p(·) ∈ L(Ω) : div p(·) = gv(·, u(·)) and, for...

Necessary and Sufficient conditions for Existence of Solutions of a Divergence-type Variational Problem

We look for necessary and sufficient conditions for the existence of solutions of the minimization problem (P) inf Ω f (P Du(x)) dx : u ∈ u ζ 0 + W m,∞ 0 (Ω; R N) where P D is a particular type of differential operator of order m, (which we identify as of divergence type) and the boundary data u ζ 0 satisfes P Du ζ 0 (x) = ζ0 for ζ0 ∈ R given.

Necessary and Sucient Optimality Conditions for a Control Fuzzy Linear Problem

Variational necessary and sufficient stability conditions for inviscid shear flow.

A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that unstable eigenvalues of Rayleigh's equation (which is a non-self-adjoint eigenvalue problem) can be associated with positive eigenvalues of a certain self-adjoint ...