Abstract
The paper deals with the change of integration for integrals∫0∞b(t)∫0tA(s)dsmdt,∫0∞A(t)∫t∞b(s)ds1/mdt,where m>0 and A,b are continuous nonnegative functions on [0,∞). There are given applications for the second-order differential nonlinear equations(a(t)|x′|αsgnx′)′+b(t)|x|βsgnx=0,where 0<β⩽α and a,b are continuous positive functions on [0,∞). 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.
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