Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator
In this article, we show the existence of three positive symmetric solutions for the integral boundary-value problem with $\phi$-Laplacian $$\displaylines{ (\phi(u'(t)))'+f(t,u(t),u'(t))=0,\quad t\in[0,1],\cr u(0)=u(1)=\int_0^1u(r)g(r)\,dr, }$$ where $\phi$ is an odd, increasing...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/336/abstr.html |
| _version_ | 1818942728758624256 |
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| author | Yonghong Ding |
| author_facet | Yonghong Ding |
| author_sort | Yonghong Ding |
| collection | DOAJ |
| description | In this article, we show the existence of three positive symmetric
solutions for the integral boundary-value problem with $\phi$-Laplacian
$$\displaylines{
(\phi(u'(t)))'+f(t,u(t),u'(t))=0,\quad t\in[0,1],\cr
u(0)=u(1)=\int_0^1u(r)g(r)\,dr,
}$$
where $\phi$ is an odd, increasing homeomorphism from $\mathbb{R}$ onto
$\mathbb{R}$. Our main tool is a fixed point theorem due to
Avery and Peterson. An example shows an applications of the obtained results. |
| first_indexed | 2024-12-20T07:16:03Z |
| format | Article |
| id | doaj.art-81cb5ebc984947d9b0653695aef11c8c |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T07:16:03Z |
| publishDate | 2016-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-81cb5ebc984947d9b0653695aef11c8c2022-12-21T19:48:48ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-12-012016336,19Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operatorYonghong Ding0 Tianshui Normal Univ., Tianshui, China In this article, we show the existence of three positive symmetric solutions for the integral boundary-value problem with $\phi$-Laplacian $$\displaylines{ (\phi(u'(t)))'+f(t,u(t),u'(t))=0,\quad t\in[0,1],\cr u(0)=u(1)=\int_0^1u(r)g(r)\,dr, }$$ where $\phi$ is an odd, increasing homeomorphism from $\mathbb{R}$ onto $\mathbb{R}$. Our main tool is a fixed point theorem due to Avery and Peterson. An example shows an applications of the obtained results.http://ejde.math.txstate.edu/Volumes/2016/336/abstr.htmlphi-Laplacianfixed pointconepositive symmetric solutions |
| spellingShingle | Yonghong Ding Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator Electronic Journal of Differential Equations phi-Laplacian fixed point cone positive symmetric solutions |
| title | Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator |
| title_full | Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator |
| title_fullStr | Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator |
| title_full_unstemmed | Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator |
| title_short | Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator |
| title_sort | existence of positive symmetric solutions for an integral boundary value problem with phi laplacian operator |
| topic | phi-Laplacian fixed point cone positive symmetric solutions |
| url | http://ejde.math.txstate.edu/Volumes/2016/336/abstr.html |
| work_keys_str_mv | AT yonghongding existenceofpositivesymmetricsolutionsforanintegralboundaryvalueproblemwithphilaplacianoperator |