On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation
This paper presents two methods to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second-order half-linear differential equation (p(x)Φ(y'))'+q(x)Φ(y)=0, with p(x) and q(x) piecewise continuous and p(x)>0, Φ(t)=|t|r-2t and r being...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/787920 |
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| _version_ | 1832545950099308544 |
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| author | Pedro Almenar Lucas Jódar |
| author_facet | Pedro Almenar Lucas Jódar |
| author_sort | Pedro Almenar |
| collection | DOAJ |
| description | This paper presents two methods to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second-order half-linear differential equation (p(x)Φ(y'))'+q(x)Φ(y)=0, with p(x) and q(x) piecewise continuous and p(x)>0, Φ(t)=|t|r-2t and r being real such that r>1. It also compares between them in several examples. Lower bounds (i.e., Lyapunov inequalities) for such a distance are also provided and compared with other methods. |
| format | Article |
| id | doaj-art-cbbc0e792b1a481596aa9a83de4bb9eb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cbbc0e792b1a481596aa9a83de4bb9eb2025-02-03T07:24:17ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/787920787920On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential EquationPedro Almenar0Lucas Jódar1Division of Network, Vodafone Spain S. A., P. E. Castellana Norte, 28050 Madrid, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainThis paper presents two methods to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second-order half-linear differential equation (p(x)Φ(y'))'+q(x)Φ(y)=0, with p(x) and q(x) piecewise continuous and p(x)>0, Φ(t)=|t|r-2t and r being real such that r>1. It also compares between them in several examples. Lower bounds (i.e., Lyapunov inequalities) for such a distance are also provided and compared with other methods.http://dx.doi.org/10.1155/2012/787920 |
| spellingShingle | Pedro Almenar Lucas Jódar On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation Abstract and Applied Analysis |
| title | On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation |
| title_full | On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation |
| title_fullStr | On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation |
| title_full_unstemmed | On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation |
| title_short | On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation |
| title_sort | on the zeroes and the critical points of a solution of a second order half linear differential equation |
| url | http://dx.doi.org/10.1155/2012/787920 |
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