# Conditional oscillation of half-linear differential equations with periodic coefficients

Archivum Mathematicum (2008)

- Volume: 044, Issue: 2, page 119-131
- ISSN: 0044-8753

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topHasil, Petr. "Conditional oscillation of half-linear differential equations with periodic coefficients." Archivum Mathematicum 044.2 (2008): 119-131. <http://eudml.org/doc/250438>.

@article{Hasil2008,

abstract = {We show that the half-linear differential equation
\[ \big [r(t)\Phi (x^\{\prime \})\big ]^\{\prime \} + \frac\{s(t)\}\{t^p\} \Phi (x) = 0 \ast \]
with $\alpha $-periodic positive functions $r, s$ is conditionally oscillatory, i.e., there exists a constant $K>0$ such that () with $\frac\{\gamma s(t)\}\{t^p\}$ instead of $\frac\{s(t)\}\{t^p\}$ is oscillatory for $\gamma > K$ and nonoscillatory for $\gamma < K$.},

author = {Hasil, Petr},

journal = {Archivum Mathematicum},

keywords = {oscillation theory; conditional oscillation; half-linear differential equations; oscillation theory; conditional oscillation; half-linear differential equation},

language = {eng},

number = {2},

pages = {119-131},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Conditional oscillation of half-linear differential equations with periodic coefficients},

url = {http://eudml.org/doc/250438},

volume = {044},

year = {2008},

}

TY - JOUR

AU - Hasil, Petr

TI - Conditional oscillation of half-linear differential equations with periodic coefficients

JO - Archivum Mathematicum

PY - 2008

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 044

IS - 2

SP - 119

EP - 131

AB - We show that the half-linear differential equation
\[ \big [r(t)\Phi (x^{\prime })\big ]^{\prime } + \frac{s(t)}{t^p} \Phi (x) = 0 \ast \]
with $\alpha $-periodic positive functions $r, s$ is conditionally oscillatory, i.e., there exists a constant $K>0$ such that () with $\frac{\gamma s(t)}{t^p}$ instead of $\frac{s(t)}{t^p}$ is oscillatory for $\gamma > K$ and nonoscillatory for $\gamma < K$.

LA - eng

KW - oscillation theory; conditional oscillation; half-linear differential equations; oscillation theory; conditional oscillation; half-linear differential equation

UR - http://eudml.org/doc/250438

ER -

## References

top- Došlý, O., Řehák, P., Half-Linear Differential Equations, Elsevier, Mathematics Studies 202, 2005. (2005) Zbl1090.34001MR2158903
- Schmidt, K. M., 10.1090/S0002-9939-99-05069-8, Proc. Amer. Math. Soc. 127 (1999), 2367–2374. (1999) Zbl0918.34039MR1626474DOI10.1090/S0002-9939-99-05069-8

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