Necessary Conditions for Solutions to Variational Problems

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...

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 Optimality Conditions for Optimization Problems with Variational Inequality Constraints

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Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

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.