Qualitative properties of solutions for the Euler equation and solvability of one-dimensional regular variational problems in the classical sense
type: Item
instance of: scholarly article
title: Qualitative properties of solutions for the Euler equation and solvability of one-dimensional regular variational problems in the classical sense
zbMATH Open document ID: 0857.49001
DOI: 10.1007/BF02107333
published in: Siberian Mathematical Journal
publication date: 1997-03-12T00:00:00Z
review text: The author gives sufficient conditions for the existence of a solution for a standard one-dimensional variational problem with integrand \(f=f(t,u,\dot u)\), \(f\in C^1(R^3)\), which is strictly convex with respect to \(\dot u\). These conditions are mainly expressed by terms of the existence of solutions of the corresponding Euler equation with specific properties -- analogously as in the approach of the lower and upper functions.
Mathematics Subject Classification ID: 49J05
Mathematics Subject Classification ID: 49N60
zbMATH DE Number: 923544
zbMATH Keywords: existence of solutions
zbMATH Keywords: one-dimensional variational problem
zbMATH Keywords: Euler equation
author: M. A. Sychev
reviewed by: Uldis Raitums
MaRDI profile type: Publication
Wikidata QID: Q112879238
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description: scientific article; zbMATH DE number 923544