Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales
In this paper, we focus on the existence of positive solutions for a boundary value problem of the changing-sign differential equation on time scales. By constructing a translation transformation and combining with the properties of the solution of the nonhomogeneous boundary value problem, we trans...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/6/315 |
| _version_ | 1827660278170386432 |
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| author | Hui Tian Xinguang Zhang Yonghong Wu Benchawan Wiwatanapataphee |
| author_facet | Hui Tian Xinguang Zhang Yonghong Wu Benchawan Wiwatanapataphee |
| author_sort | Hui Tian |
| collection | DOAJ |
| description | In this paper, we focus on the existence of positive solutions for a boundary value problem of the changing-sign differential equation on time scales. By constructing a translation transformation and combining with the properties of the solution of the nonhomogeneous boundary value problem, we transfer the changing-sign problem to a positone problem, then by means of the known fixed-point theorem, several sufficient conditions for the existence of positive solutions are established for the case in which the nonlinear term of the equation may change sign. |
| first_indexed | 2024-03-09T23:46:36Z |
| format | Article |
| id | doaj.art-44b725bca04845e49e37b257253fb2be |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T23:46:36Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-44b725bca04845e49e37b257253fb2be2023-11-23T16:42:40ZengMDPI AGFractal and Fractional2504-31102022-06-016631510.3390/fractalfract6060315Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time ScalesHui Tian0Xinguang Zhang1Yonghong Wu2Benchawan Wiwatanapataphee3School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, ChinaSchool of Mathematical and Informational Sciences, Yantai University, Yantai 264005, ChinaDepartment of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, AustraliaDepartment of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, AustraliaIn this paper, we focus on the existence of positive solutions for a boundary value problem of the changing-sign differential equation on time scales. By constructing a translation transformation and combining with the properties of the solution of the nonhomogeneous boundary value problem, we transfer the changing-sign problem to a positone problem, then by means of the known fixed-point theorem, several sufficient conditions for the existence of positive solutions are established for the case in which the nonlinear term of the equation may change sign.https://www.mdpi.com/2504-3110/6/6/315positive solutionschanging signfixed-point theoremtime scalescone |
| spellingShingle | Hui Tian Xinguang Zhang Yonghong Wu Benchawan Wiwatanapataphee Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales Fractal and Fractional positive solutions changing sign fixed-point theorem time scales cone |
| title | Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales |
| title_full | Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales |
| title_fullStr | Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales |
| title_full_unstemmed | Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales |
| title_short | Existence of Positive Solutions for a Singular Second-Order Changing-Sign Differential Equation on Time Scales |
| title_sort | existence of positive solutions for a singular second order changing sign differential equation on time scales |
| topic | positive solutions changing sign fixed-point theorem time scales cone |
| url | https://www.mdpi.com/2504-3110/6/6/315 |
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