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Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II
Archivum mathematicum, Tome 57 (2021) no. 1, pp. 41-60 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider the half-linear differential equation of the form \[ (p(t)|x^{\prime }|^{\alpha }\mathrm{sgn}\,x^{\prime })^{\prime } + q(t)|x|^{\alpha }\mathrm{sgn}\,x = 0\,, \quad t \ge t_{0} \,, \] under the assumption that $p(t)^{-1/\alpha }$ is integrable on $[t_{0}, \infty )$. 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 \rightarrow \infty $.
We consider the half-linear differential equation of the form \[ (p(t)|x^{\prime }|^{\alpha }\mathrm{sgn}\,x^{\prime })^{\prime } + q(t)|x|^{\alpha }\mathrm{sgn}\,x = 0\,, \quad t \ge t_{0} \,, \] under the assumption that $p(t)^{-1/\alpha }$ is integrable on $[t_{0}, \infty )$. 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 \rightarrow \infty $.
DOI : 10.5817/AM2021-1-41
Classification : 26D10, 34C10, 34C11
Keywords: asymptotic behavior; nonoscillatory solution; half-linear differential equation; Hardy-type inequality 
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Naito, Manabu. Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II. Archivum mathematicum, Tome 57 (2021) no. 1, pp. 41-60. doi: 10.5817/AM2021-1-41

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