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Integral averages and oscillation of second order sublinear differential equations

Authors:

Jelena V. Manojlović

Affiliation:

(1) Faculty of Science and Mathematics, University of Ni "scaron"

, Vi

egradska 33, 180 00 Ni "scaron"

, Yugoslavia

Abstract:

New oscillation criteria are given for the second order sublinear differential equation

$left[ {aleft( t right)psi left( {xleft( t right)} right)x'left( t right)} right] + qleft( t right)fleft( {xleft( t right)} right) = 0,t geqslant t_0 > 0,$

where a

C¹ ([t₀,

)) is a nonnegative function, psgr

, f

) with

(x)

0, xf(x) / psgr

(x) > 0 for x

, f have continuous derivative on Ropf

{0} with [f(x) / #x03C8;(x)] prime

0 for x

0 and q

C([t₀,

)) has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x Prime

(t) + q(t)x(t) = 0.

Keywords:

oscillation sublinear differential equation integral averages

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