Oscillation constant for modified Euler type half-linear equations
Applying the modified half-linear Prufer angle, we study oscillation properties of the half-linear differential equation $$ [ r(t) t^{p-1} \Phi(x')]' + \frac{s(t)}{t \log^pt} \Phi(x) = 0, \quad \Phi(x)=|x|^{p-1}\hbox{sgn} x. $$ We show that this equation is conditionally oscillatory...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/220/abstr.html |
| Summary: | Applying the modified half-linear Prufer angle, we study oscillation
properties of the half-linear differential equation
$$
[ r(t) t^{p-1} \Phi(x')]' + \frac{s(t)}{t \log^pt} \Phi(x) = 0, \quad
\Phi(x)=|x|^{p-1}\hbox{sgn} x.
$$
We show that this equation is conditionally oscillatory in a very general case.
Moreover, we identify the critical oscillation constant
(the borderline depending on the functions r and s which separates
the oscillatory and non-oscillatory equations).
Note that the used method is different from the standard method based
on the half-linear Prufer angle. |
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| ISSN: | 1072-6691 |