Integral averages and oscillation of second order sublinear differential equations |
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| Authors: | Jelena V Manojlovi? |
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| Institution: | (1) Faculty of Science and Mathematics, University of Ni , Viegradska 33, 180 00 Ni, Yugoslavia |
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| Abstract: | New oscillation criteria are given for the second order sublinear differential equation where a  C
1 (t
0,  )) is a nonnegative function,  , f C( ) with (x)  0, xf(x) / (x) > 0 for x 0, , f have continuous derivative on \ {0} with f(x) / #x03C8;(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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| Keywords: | oscillation sublinear differential equation integral averages |
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![$$\left {a\left( t \right)\psi \left( {x\left( t \right)} \right)x'\left( t \right)} \right] + q\left( t \right)f\left( {x\left( t \right)} \right) = 0,t \geqslant t_0 > 0,$$](/content/u6h5157336456016/10587_2005_Article_3_TeX2GIFEqu1.gif)