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ON THE ZEROS OF SOLUTIONS OF THE DIFFERENTIAL EQUATION ω(2m) + p(z)ω = 0

ON THE ZEROS OF SOLUTIONS OF THE DIFFERENTIAL EQUATION ω(2m) + p(z)ω = 0 DEMONSTRATIO MATHEMATICAVol. XXXVNo 12002G. M. MuminovON THE ZEROS OF SOLUTIONSOF T H E D I F F E R E N T I A L EQUATION u/ 2 m ) +p(z)u> = 01. We consider a linear differential equation of order n:(1)W(n) + Pl(z)u/n-1)+ . . . + pn(z)<jJ = 0,where the complex-valued functions Pk(z), k = 1 , 2 , . . . ,n are analytic functions which are regular in a region D of the complex plane.The differential equation (1) is said to be disconjugate in D if no nontrivial solution of (1) has more than n—1 zeros (where the zeros axe counted withtheir multiplicities) in D. The equation (1) is said to be (m, m)-disconjugatein D if n — 2m and if no nontrivial solution of (1) has two zeros of order min D.In [1] the following result for differential equations of arbitrary even orderwas obtained:THEOREM A. The differential(2)equationw(2m) +p(z)u= 0,where the function p(z) is analytic in \z\ < 1, is (m,m)-disconjugate,\P(Z)\ <where B(2) = 1, B(4) = 9 andmB(2m) = 9 JJ(4A; — 3),fc=3In [2] the following result was obtained:m = 3,4,..if42G. M. M u m i n o vTHEOREM B. The differential equation (2), http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON THE ZEROS OF SOLUTIONS OF THE DIFFERENTIAL EQUATION ω(2m) + p(z)ω = 0

Muminov, G. M.
Demonstratio Mathematica , Volume 35 (1): 8 – Jan 1, 2002
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References (3)

Publisher
de Gruyter
Copyright
© by G. M. Muminov
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2002-0107
Publisher site
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Abstract

DEMONSTRATIO MATHEMATICAVol. XXXVNo 12002G. M. MuminovON THE ZEROS OF SOLUTIONSOF T H E D I F F E R E N T I A L EQUATION u/ 2 m ) +p(z)u> = 01. We consider a linear differential equation of order n:(1)W(n) + Pl(z)u/n-1)+ . . . + pn(z)<jJ = 0,where the complex-valued functions Pk(z), k = 1 , 2 , . . . ,n are analytic functions which are regular in a region D of the complex plane.The differential equation (1) is said to be disconjugate in D if no nontrivial solution of (1) has more than n—1 zeros (where the zeros axe counted withtheir multiplicities) in D. The equation (1) is said to be (m, m)-disconjugatein D if n — 2m and if no nontrivial solution of (1) has two zeros of order min D.In [1] the following result for differential equations of arbitrary even orderwas obtained:THEOREM A. The differential(2)equationw(2m) +p(z)u= 0,where the function p(z) is analytic in \z\ < 1, is (m,m)-disconjugate,\P(Z)\ <where B(2) = 1, B(4) = 9 andmB(2m) = 9 JJ(4A; — 3),fc=3In [2] the following result was obtained:m = 3,4,..if42G. M. M u m i n o vTHEOREM B. The differential equation (2),

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 2002

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