Address. Department of Mathematics, Masaryk University, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC
Abstract. In this paper we study extremal properties of functional associated with the half--linear second order differential equation \Ep. Necessary and sufficient condition for nonnegativity of this functional is given in two special cases: the first case is when both points are regular and the second is the case, when one end point is singular. The obtained results extend the theory of quadratic functionals.
AMSclassification. 34C10, 49K15
Keywords. Half--linear differential equation, associated functional, Picone identity, conjugate points