Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
Keyword(s):
We consider the half-linear differential equation of the form \[(p(t)|x'|^{\alpha}\mathrm{sgn} x')' + q(t)|x|^{\alpha}\mathrm{sgn} x = 0, \quad t\geq t_{0},\] under the assumption \(\int_{t_{0}}^{\infty}p(s)^{-1/\alpha}ds =\infty\). It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as \(t \to \infty\).
2008 ◽
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2011 ◽
Vol 381
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pp. 315-327
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1978 ◽
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pp. 394-398
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2013 ◽
Vol 21
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