Summary: Here, a relation between integrals and variational multipliers of a system of second-order ordinary differential equations is studied. A simple necessary and sufficient local condition for the existence of a multiplier is given.
@article{701673, title = {Integrals and variational multipliers of second-order ordinary differential equations}, booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"}, series = {GDML\_Books}, publisher = {Circolo Matematico di Palermo}, address = {Palermo}, year = {2001}, pages = {129-131}, mrnumber = {MR1826685}, zbl = {0983.34004}, url = {http://dml.mathdoc.fr/item/701673} }
Klapka, Lubomír. Integrals and variational multipliers of second-order ordinary differential equations, dans Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books, (2001), pp. 129-131. http://gdmltest.u-ga.fr/item/701673/