On the theory of discontinuous solutions of variational problems in the class of generalized curves (Q1599411)

The paper deals with the variational problem \(\inf \int_a^b F(x,y,y')\,dy\) over the class of discontinuous functions \(y=y(x)\). Here \(F(x,y,z)>0\), \(F(x,y,z)\) is convex in \(z\) and \(\lim_{z\to \pm \infty} z^{-1} F(x,y,z)\) exists for all \((x,y)\). The authors prove that the problem possesses a generalized solution.