Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative
Using the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $m$-point boundary-value problem $$displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,quad 0<t<1,cr x'(0)=0,quad x(1)= sum_{i=1}^{m-2}a_{i}x(xi_i), }$$ wher...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2008-10-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2008/147/abstr.html |
| _version_ | 1818152125083942912 |
|---|---|
| author | Baoqiang Yan Ya Ma |
| author_facet | Baoqiang Yan Ya Ma |
| author_sort | Baoqiang Yan |
| collection | DOAJ |
| description | Using the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $m$-point boundary-value problem $$displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,quad 0<t<1,cr x'(0)=0,quad x(1)= sum_{i=1}^{m-2}a_{i}x(xi_i), }$$ where $0<xi_1<xi_2<dots<xi_{m-2}<1$, $a_iin [0,1)$, $i = 1, 2,dots, m-2$, with $0< sum_{i=1}^{m-2}a_i <1 $ and $f$ maybe singular at $x=0$ and $x'=0$. |
| first_indexed | 2024-12-11T13:49:44Z |
| format | Article |
| id | doaj.art-0fe25d4dec5a4b75bc55218a66052ab2 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T13:49:44Z |
| publishDate | 2008-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-0fe25d4dec5a4b75bc55218a66052ab22022-12-22T01:04:19ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912008-10-012008147,128Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivativeBaoqiang YanYa MaUsing the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $m$-point boundary-value problem $$displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,quad 0<t<1,cr x'(0)=0,quad x(1)= sum_{i=1}^{m-2}a_{i}x(xi_i), }$$ where $0<xi_1<xi_2<dots<xi_{m-2}<1$, $a_iin [0,1)$, $i = 1, 2,dots, m-2$, with $0< sum_{i=1}^{m-2}a_i <1 $ and $f$ maybe singular at $x=0$ and $x'=0$.http://ejde.math.txstate.edu/Volumes/2008/147/abstr.htmlm-point boundary-value problemsingularitypositive solutionsfixed point theorem |
| spellingShingle | Baoqiang Yan Ya Ma Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative Electronic Journal of Differential Equations m-point boundary-value problem singularity positive solutions fixed point theorem |
| title | Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative |
| title_full | Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative |
| title_fullStr | Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative |
| title_full_unstemmed | Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative |
| title_short | Multiple positive solutions for singular m-point boundary-value problems with nonlinearities depending on the derivative |
| title_sort | multiple positive solutions for singular m point boundary value problems with nonlinearities depending on the derivative |
| topic | m-point boundary-value problem singularity positive solutions fixed point theorem |
| url | http://ejde.math.txstate.edu/Volumes/2008/147/abstr.html |
| work_keys_str_mv | AT baoqiangyan multiplepositivesolutionsforsingularmpointboundaryvalueproblemswithnonlinearitiesdependingonthederivative AT yama multiplepositivesolutionsforsingularmpointboundaryvalueproblemswithnonlinearitiesdependingonthederivative |