Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations
We consider the half-linear differential equation \[(|x'|^{\alpha}\mathrm{sgn}\,x')' + q(t)|x|^{\alpha}\mathrm{sgn}\,x = 0, \quad t \geq t_{0},\] under the condition \[\lim_{t\to\infty}t^{\alpha}\int_{t}^{\infty}q(s)ds = \frac{\alpha^{\alpha}}{(\alpha+1)^{\alpha+1}}.\] It is shown tha...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2023-03-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol43/2/art/opuscula_math_4313.pdf |