Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations
The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z), B (z) and F (z) are meromorphic functions with finite order having only finitely many poles. We show that,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2016-04-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/676 |
| _version_ | 1818656648079605760 |
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| author | Maamar Andasmas Benharrat Belaidi |
| author_facet | Maamar Andasmas Benharrat Belaidi |
| author_sort | Maamar Andasmas |
| collection | DOAJ |
| description | The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z), B (z) and F (z) are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z)| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B), ρ(F)} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. |
| first_indexed | 2024-12-17T03:28:55Z |
| format | Article |
| id | doaj.art-032f6d7392db41a991dc56064d9c61e4 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-17T03:28:55Z |
| publishDate | 2016-04-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-032f6d7392db41a991dc56064d9c61e42022-12-21T22:05:19ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392016-04-011111118169Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential EquationsMaamar AndasmasBenharrat BelaidiThe main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z), B (z) and F (z) are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z)| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B), ρ(F)} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.http://etamaths.com/index.php/ijaa/article/view/676 |
| spellingShingle | Maamar Andasmas Benharrat Belaidi Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations International Journal of Analysis and Applications |
| title | Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations |
| title_full | Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations |
| title_fullStr | Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations |
| title_full_unstemmed | Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations |
| title_short | Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations |
| title_sort | growth and zeros of meromorphic solutions to second order linear differential equations |
| url | http://etamaths.com/index.php/ijaa/article/view/676 |
| work_keys_str_mv | AT maamarandasmas growthandzerosofmeromorphicsolutionstosecondorderlineardifferentialequations AT benharratbelaidi growthandzerosofmeromorphicsolutionstosecondorderlineardifferentialequations |