Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation
In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscil...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/502 |
| _version_ | 1797416636181905408 |
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| author | Zuzana Pátíková |
| author_facet | Zuzana Pátíková |
| author_sort | Zuzana Pátíková |
| collection | DOAJ |
| description | In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation). |
| first_indexed | 2024-03-09T06:07:02Z |
| format | Article |
| id | doaj.art-25cdcd11e14c4c3896bb4f36138eabb9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T06:07:02Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-25cdcd11e14c4c3896bb4f36138eabb92023-12-03T12:02:26ZengMDPI AGMathematics2227-73902021-03-019550210.3390/math9050502Integral Comparison Criteria for Half-Linear Differential Equations Seen as a PerturbationZuzana Pátíková0Department of Mathematics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 760 05 Zlín, Czech RepublicIn this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation).https://www.mdpi.com/2227-7390/9/5/502half-linear differential equationoscillation criteriamodified Riccati techniqueEuler-type equationsecond-order differential equation |
| spellingShingle | Zuzana Pátíková Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation Mathematics half-linear differential equation oscillation criteria modified Riccati technique Euler-type equation second-order differential equation |
| title | Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation |
| title_full | Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation |
| title_fullStr | Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation |
| title_full_unstemmed | Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation |
| title_short | Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation |
| title_sort | integral comparison criteria for half linear differential equations seen as a perturbation |
| topic | half-linear differential equation oscillation criteria modified Riccati technique Euler-type equation second-order differential equation |
| url | https://www.mdpi.com/2227-7390/9/5/502 |
| work_keys_str_mv | AT zuzanapatikova integralcomparisoncriteriaforhalflineardifferentialequationsseenasaperturbation |