$napis="Abstract"; include "zacatek.inc"; ?> Preprint GA 4/2003
Given a dynamical form $E'$, we can ask if there is a locally variational form, equivalent with $E'$. The integrating factor $G$ such that $E=GE'$ is locally variational form is then called a variational integrating factor. A complete solution of problem of searching for variational integrating factors in general is yet not known. There have been achieved some particular results concerning mainly second-order ODE. Concerning PDE, there is only one paper containing a short remark on a solution of the multiplier problem for a single second order partial diffferential equation.
The aim of this work is to study the problem of variational integrating factors for a dynamical form, which represents a system of first order PDE. We prove that if an everywhere regular matrix $G$ is a variational integrating factor for a regular variational form $E'$, then $E=GE'$ is regular and the ideals associated dynamical differential coincide. We find a system of equations for variational integrating factors by the assumption that $E'$ is a polynomial in first derivatives. Finally we compute concrete conditions for variational integrating factors in two special case include "konec.inc"; ?>