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Growth and oscillation related to a second order linear differential equation

Benharrat Belaϊdi ; of Mostaganem ,Mostaganem, Algeria


Puni tekst: engleski pdf 386 Kb

str. 171-184

preuzimanja: 652

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Sažetak

This paper is devoted to studying the growth and the oscillation of
solutions of the second order non-homogeneous linear differential equation
\begin{equation*}
f^{\prime \prime }+A_{1}\left( z\right) e^{P\left( z\right) }f^{\prime
}+A_{0}\left( z\right) e^{Q\left( z\right) }f=F,
\end{equation*}%
where $P\left( z\right)$, $Q\left( z\right) $ are nonconstant
polynomials such that $\deg P=\deg Q=n$ and $A_{j}\left( z\right) $\linebreak
$\left( \not\equiv 0\right) $ $(j=0,1),$ $F\left( z\right) $ are
entire functions with $\max \{\rho \left( A_{j}\right) :j=0,1\} investigate the relationship between small functions and differential
polynomials $g_{f}\left( z\right) \linebreak =d_{2}f^{\prime \prime }+d_{1}f^{\prime
}+d_{0}f$, where $d_{0}\left( z\right) ,d_{1}\left( z\right) ,d_{2}\left(
z\right) $ are entire functions such that at least one of $d_{0},d_{1},d_{2}$%
\ does not vanish identically with $\rho \left( d_{j}\right) $\left( j=0,1,2\right) $ generated by solutions of the above
equation.

Ključne riječi

linear differential equations; differential polynomials; entire solutions; order of growth; exponent of convergence of zeros; exponent of convergence of distinct zeros

Hrčak ID:

101436

URI

https://hrcak.srce.hr/101436

Datum izdavanja:

10.5.2013.

Posjeta: 1.273 *