Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order
In this article we study the existence of positive solutions for the nonlocal multi-point boundary-value problem $$displaylines{ u''(t)+f(t, ^{c}D^{alpha}u(t))=0, quad alpha in(0, 1), ext{ a.e. } tin(0, 1), cr u(0)=0, quad u(1)=sum_{k=1}^m a_k u(au_k), quad au_kin(a, b)subset (0, 1)....
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-03-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/64/abstr.html |
| _version_ | 1811249763447734272 |
|---|---|
| author | Ahmed M. A. El-Sayed Ebtisam O. Bin-Taher |
| author_facet | Ahmed M. A. El-Sayed Ebtisam O. Bin-Taher |
| author_sort | Ahmed M. A. El-Sayed |
| collection | DOAJ |
| description | In this article we study the existence of positive solutions for the nonlocal multi-point boundary-value problem $$displaylines{ u''(t)+f(t, ^{c}D^{alpha}u(t))=0, quad alpha in(0, 1), ext{ a.e. } tin(0, 1), cr u(0)=0, quad u(1)=sum_{k=1}^m a_k u(au_k), quad au_kin(a, b)subset (0, 1). }$$ We also consider the corresponding integral condition, and the two special cases $alpha = 0 $ and $ alpha = 1$. |
| first_indexed | 2024-04-12T15:53:19Z |
| format | Article |
| id | doaj.art-db31755a6fd144fa94baa6b2a6d00379 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T15:53:19Z |
| publishDate | 2013-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-db31755a6fd144fa94baa6b2a6d003792022-12-22T03:26:27ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-03-01201364,18Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second orderAhmed M. A. El-SayedEbtisam O. Bin-TaherIn this article we study the existence of positive solutions for the nonlocal multi-point boundary-value problem $$displaylines{ u''(t)+f(t, ^{c}D^{alpha}u(t))=0, quad alpha in(0, 1), ext{ a.e. } tin(0, 1), cr u(0)=0, quad u(1)=sum_{k=1}^m a_k u(au_k), quad au_kin(a, b)subset (0, 1). }$$ We also consider the corresponding integral condition, and the two special cases $alpha = 0 $ and $ alpha = 1$.http://ejde.math.txstate.edu/Volumes/2013/64/abstr.htmlFractional calculusboundary value problemnonlocal conditionintegral conditionpositive solution |
| spellingShingle | Ahmed M. A. El-Sayed Ebtisam O. Bin-Taher Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order Electronic Journal of Differential Equations Fractional calculus boundary value problem nonlocal condition integral condition positive solution |
| title | Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order |
| title_full | Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order |
| title_fullStr | Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order |
| title_full_unstemmed | Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order |
| title_short | Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order |
| title_sort | positive solutions for a nonlocal multi point boundary value problem of fractional and second order |
| topic | Fractional calculus boundary value problem nonlocal condition integral condition positive solution |
| url | http://ejde.math.txstate.edu/Volumes/2013/64/abstr.html |
| work_keys_str_mv | AT ahmedmaelsayed positivesolutionsforanonlocalmultipointboundaryvalueproblemoffractionalandsecondorder AT ebtisamobintaher positivesolutionsforanonlocalmultipointboundaryvalueproblemoffractionalandsecondorder |