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Integral averages and oscillation of second order sublinear differential equations

Jelena V. Manojlović — 2005

Czechoslovak Mathematical Journal

New oscillation criteria are given for the second order sublinear differential equation [ a ( t ) ψ ( x ( t ) ) x ' ( t ) ] ' + q ( t ) f ( x ( t ) ) = 0 , t t 0 > 0 , where a C 1 ( [ t 0 , ) ) is a nonnegative function, ψ , f C ( ) with ψ ( x ) 0 , x f ( x ) / ψ ( x ) > 0 for x 0 , ψ , f have continuous derivative on { 0 } with [ f ( x ) / ψ ( x ) ] ' 0 for x 0 and q C ( [ t 0 , ) ) 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 ' ' ( t ) + q ( t ) x ( t ) = 0 .

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