Geodesic
On solvability of certain classes of irregular the second order variation problems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 2, pp. 32-36.

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In the work the irregular model $-p(x)u'(x)+p(+0)u'(+0)+\int_0^xu(\tau)\,dQ(\tau)=F(x)-F(0)$ of the Stiltjes string on segment $[0,\ell]$ with boundary conditions $u(0)=u(\ell)=0$ is discussed. The solvability conditions of the mentioned problem are described. 
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Yu. V. Pokornyi; Zh. I. Bakhtina; A. S. Ishchenko. On solvability of certain classes of irregular the second order variation problems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 2, pp. 32-36. http://geodesic.mathdoc.fr/item/ISU_2007_7_2_a6/

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