Conditions nécessaires et suffisantes d'existence de solutions en calcul des variations. (Necessary and sufficient conditions for the existence of solutions in the calculus of variations)

DOI10.1016/S0294-1449(16)30371-7zbMath0641.49012MaRDI QIDQ1100721

Jean-Pierre Raymond

Publication date: 1987

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1987__4_2_169_0

zbMATH Keywords

variational problemrelaxed problempseudo-Hamiltonian

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Optimality conditions for problems involving ordinary differential equations (49K15) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items

Strong compactness in Sobolev spaces, On a classical problem of the calculus of variations without convexity assumptions, Another theorem of classical solvability `in small' for one-dimensional variational problems, Existence of scalar minimizers for nonconvex simple integrals of sum type, Existence and regularity for scalar minimizers of affine nonconvex simple integrals.

Cites Work

• One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
• Discontinuites de champs hamiltoniens et existence de solutions optimales en calcul des variations
• Théoremes d'existence pour des problèmes du calcul des variations du type: \(\text{Inf}\int^L_0f(x,u'(x))dx\) et \(\text{Inf} \int^L_0f(x,u(x),u'(x))dx\).
• Broken solutions of homogeneous variational problems
• Optimization and nonsmooth analysis
• The Generalized Problem of Bolza
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