ON THE POTENTIALITY OF A CLASS OF OPERATORS RELATIVE TO LOCAL BILINEAR FORMS

The inverse problem of the calculus variations (IPCV) is solved for a second-order ordinary differential equation with use local bilinear form. We apply methods analytical dynamics, nonlinear functional analysis, and modern solving IPCV. In paper, we obtain necessary sufficient conditions given operator to be potential relative form, construct corresponding functional, i.e., found solution IPCV, define structure considered operator. As consequence, similar results are obtained when using nonlocal Theoretical illustrated some examples.