Qualitative properties of solutions for the Euler equation and solvability of one-dimensional regular variational problems in the classical sense
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.
scientific article; zbMATH DE number 923544
scientific article