ON A MINIMIZATION PROBLEM FOR A FUNCTIONAL GENERATED BY THE STURM – LIOUVILLE PROBLEM WITH INTEGRAL CONDITION ON THE POTENTIAL

In this article we consider the minimization problem of the functional generated by a Sturm — Liouville problem with Dirichlet boundary conditions and with an integral condition on the potential. Estimation of the infimum of functional in some class of functions y and Q(x) is
reduced to estimation of a nonlinear functional non depending on the potential Q(x). This leads to related parameterized nonlinear boundary value problem. Upper and lower estimates are obtained for different values of parameter.