On the theory of conjugate points for parameter-invariant higher order problems in the calculus of variations

1968 ◽  
Vol 79 (1) ◽  
pp. 71-92
Author(s):  
H. S. P. Grässer
Keyword(s):  
Calculus Of Variations ◽  
Higher Order ◽  
Conjugate Points

scholarly journals The classical theory of calculus of variations for generalized functions

2017 ◽  
Vol 8 (1) ◽  
pp. 779-808 ◽  
Author(s):  
Alexander Lecke ◽  
Lorenzo Luperi Baglini ◽  
Paolo Giordano
Keyword(s):  
Calculus Of Variations ◽  
Classical Theory ◽  
Sufficient Conditions ◽  
Generalized Functions ◽  
Conjugate Points ◽  
Lagrange Equations ◽  
Smooth Functions ◽  
Nonlinear Properties ◽  
Schwartz Distributions ◽  
Necessary And Sufficient

Abstract We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary smooth functions. We prove full connections between extremals and Euler–Lagrange equations, classical necessary and sufficient conditions to have a minimizer, the necessary Legendre condition, Jacobi’s theorem on conjugate points and Noether’s theorem. We close with an application to low regularity Riemannian geometry.

scholarly journals Optimality conditions for the calculus of variations with higher-order delta derivatives

2011 ◽  
Vol 24 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Rui A.C. Ferreira ◽  
Agnieszka B. Malinowska ◽  
Delfim F.M. Torres
Keyword(s):  
Optimality Conditions ◽  
Calculus Of Variations ◽  
Higher Order ◽  
Delta Derivatives

scholarly journals Composition functionals in higher order calculus of variations and Noether's theorem

2021 ◽  
pp. 1-18
Author(s):  
Gastão S. F. Frederico ◽  
J. Vanterler da C. Sousa ◽  
Ricardo Almeida
Keyword(s):  
Calculus Of Variations ◽  
Higher Order ◽  
Noether’S Theorem ◽  
Noether's Theorem
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