On an extension of the Fubini theorem and its applications in ODEs

摘要

The paper deals with the change of integration for integralsintegral(0)(infinity)b(t) (integral(0)(t), A(s) ds)(m) dt, integral(0)(infinity) A(t) (integral(t)(infinity) b(s) ds)(1/m) dt,where m > 0 and A, b are continuous nonnegative functions on [0, infinity). There are given applications for the second-order differential nonlinear equations(a(t)x(alpha) s gnx')'+b(t)x(beta) sgn x = 0,where 0 < beta less than or equal to alpha and a, b are continuous positive functions on [0, infinity). The first application brings comparison results for oscillation of two generalized Emden-Fowler equations, the second one shows the similarities and discrepancies for nonoscillatory half-linear and linear differential equations. (C) 2004 Elsevier Ltd. All rights reserved.