Necessary conditions and non-existence results for autonomous nonconvex variational problems

Necessary and Sufficient Conditions for Optimality of Nonconvex, Noncoercive Autonomous Variational Problems with Constraints

We consider the classical autonomous constrained variational problem of minimization of ∫ b a f(v(t), v ′(t))dt in the class Ω:={v ∈ W 1,1(a, b) : v(a) = α, v(b) = β, v′(t) ≥ 0 a.e. in (a, b)}, where f : [α, β] × [0,+∞) → R is a lower semicontinuous, nonnegative integrand, which can be nonsmooth, nonconvex and noncoercive. We prove a necessary and sufficient condition for the optimality of a tr...

Existence Theorems for Nonconvex Variational Inequalities Problems

In this paper, we prove the existence theorem for a mapping defined by T = T1 + T2 when T1 is a μ1-Lipschitz continuous and γ-strongly monotone mapping, T2 is a μ2-Lipschitz continuous mapping, we have a mapping T is Lipschitz continuous but not strongly monotone mapping. This work is extend and improve the result of N. Petrot [17]. Mathematics Subject Classification: 46C05, 47D03, 47H09, 47H10...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

Existence results for nonconvex equilibrium problems

In this paper, we establish sufficient conditions for the existence of solutions of equilibrium problems in a metric space, that do not involve any convexity assumption either for the domain or for the function. To prove these results, a weak notion of semicontinuity is considered. Furthermore, some existence results for systems of equilibrium problems are provided.

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...