Existence of positive solutions for a nonlinear quadratic integral equation
In this article, we study the existence of positive solutions for the nonlinear quadratic integral equation $$ x(t)=g(t,x(t))\int_{-\infty}^{t}a(t,t-s)f(s,x(s))ds,\quad t\in\mathbb{R}. $$ By using fixed point theory on cones, we prove the existence and uniqueness of bounded and continuous solu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/79/abstr.html |
| _version_ | 1818437282203435008 |
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| author | Chu-Hang Wang Hui-Sheng Ding Gaston M. N'Guerekata |
| author_facet | Chu-Hang Wang Hui-Sheng Ding Gaston M. N'Guerekata |
| author_sort | Chu-Hang Wang |
| collection | DOAJ |
| description | In this article, we study the existence of positive solutions for the
nonlinear quadratic integral equation
$$
x(t)=g(t,x(t))\int_{-\infty}^{t}a(t,t-s)f(s,x(s))ds,\quad t\in\mathbb{R}.
$$
By using fixed point theory on cones, we prove the existence and uniqueness
of bounded and continuous solution with positive infimum. An example
illustrates the abstract result. |
| first_indexed | 2024-12-14T17:22:12Z |
| format | Article |
| id | doaj.art-6958652d685042a5aac145dcdeb8a372 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T17:22:12Z |
| publishDate | 2019-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-6958652d685042a5aac145dcdeb8a3722022-12-21T22:53:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-06-01201979,111Existence of positive solutions for a nonlinear quadratic integral equationChu-Hang Wang0Hui-Sheng Ding1Gaston M. N'Guerekata2 Jiangxi Normal Univ., Nanchang, Jiangxi, China Jiangxi Normal Univ., Nanchang, Jiangxi, China Morgan State Univ., Baltimore, MD, USA In this article, we study the existence of positive solutions for the nonlinear quadratic integral equation $$ x(t)=g(t,x(t))\int_{-\infty}^{t}a(t,t-s)f(s,x(s))ds,\quad t\in\mathbb{R}. $$ By using fixed point theory on cones, we prove the existence and uniqueness of bounded and continuous solution with positive infimum. An example illustrates the abstract result.http://ejde.math.txstate.edu/Volumes/2019/79/abstr.htmlQuadratic integral equationpositive solutioncone |
| spellingShingle | Chu-Hang Wang Hui-Sheng Ding Gaston M. N'Guerekata Existence of positive solutions for a nonlinear quadratic integral equation Electronic Journal of Differential Equations Quadratic integral equation positive solution cone |
| title | Existence of positive solutions for a nonlinear quadratic integral equation |
| title_full | Existence of positive solutions for a nonlinear quadratic integral equation |
| title_fullStr | Existence of positive solutions for a nonlinear quadratic integral equation |
| title_full_unstemmed | Existence of positive solutions for a nonlinear quadratic integral equation |
| title_short | Existence of positive solutions for a nonlinear quadratic integral equation |
| title_sort | existence of positive solutions for a nonlinear quadratic integral equation |
| topic | Quadratic integral equation positive solution cone |
| url | http://ejde.math.txstate.edu/Volumes/2019/79/abstr.html |
| work_keys_str_mv | AT chuhangwang existenceofpositivesolutionsforanonlinearquadraticintegralequation AT huishengding existenceofpositivesolutionsforanonlinearquadraticintegralequation AT gastonmnguerekata existenceofpositivesolutionsforanonlinearquadraticintegralequation |