Positive solutions to second-order singular nonlocal problems: existence and sharp conditions
Abstract In this paper we consider sharp conditions on ω and f for the existence of C1[0,1] $C^{1}[0,1]$ positive solutions to a second-order singular nonlocal problem u″(t)+ω(t)f(t,u(t))=0 $u''(t)+\omega (t)f(t,u(t))=0$, u(0)=u(1)=∫01g(t)u(t)dt $u(0)=u(1)=\int _{0} ^{1}g(t)u(t)\,dt$; it t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-10-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1289-7 |
| _version_ | 1818271488400162816 |
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| author | Shiqi Ma Xuemei Zhang |
| author_facet | Shiqi Ma Xuemei Zhang |
| author_sort | Shiqi Ma |
| collection | DOAJ |
| description | Abstract In this paper we consider sharp conditions on ω and f for the existence of C1[0,1] $C^{1}[0,1]$ positive solutions to a second-order singular nonlocal problem u″(t)+ω(t)f(t,u(t))=0 $u''(t)+\omega (t)f(t,u(t))=0$, u(0)=u(1)=∫01g(t)u(t)dt $u(0)=u(1)=\int _{0} ^{1}g(t)u(t)\,dt$; it turns out that this case is more difficult to handle than two point boundary value problems and needs some new ingredients in the arguments. On the technical level, we adopt the topological degree method. |
| first_indexed | 2024-12-12T21:26:58Z |
| format | Article |
| id | doaj.art-236d4d822a9a40cb868f12c52546d868 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-12T21:26:58Z |
| publishDate | 2019-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-236d4d822a9a40cb868f12c52546d8682022-12-22T00:11:26ZengSpringerOpenBoundary Value Problems1687-27702019-10-012019111810.1186/s13661-019-1289-7Positive solutions to second-order singular nonlocal problems: existence and sharp conditionsShiqi Ma0Xuemei Zhang1School of Mathematics and Physics, North China Electric Power UniversitySchool of Mathematics and Physics, North China Electric Power UniversityAbstract In this paper we consider sharp conditions on ω and f for the existence of C1[0,1] $C^{1}[0,1]$ positive solutions to a second-order singular nonlocal problem u″(t)+ω(t)f(t,u(t))=0 $u''(t)+\omega (t)f(t,u(t))=0$, u(0)=u(1)=∫01g(t)u(t)dt $u(0)=u(1)=\int _{0} ^{1}g(t)u(t)\,dt$; it turns out that this case is more difficult to handle than two point boundary value problems and needs some new ingredients in the arguments. On the technical level, we adopt the topological degree method.http://link.springer.com/article/10.1186/s13661-019-1289-7Sharp conditionsSingular boundary value problems with integral boundary conditionsHölder’s inequalityFixed point theoremsPositive solutions |
| spellingShingle | Shiqi Ma Xuemei Zhang Positive solutions to second-order singular nonlocal problems: existence and sharp conditions Boundary Value Problems Sharp conditions Singular boundary value problems with integral boundary conditions Hölder’s inequality Fixed point theorems Positive solutions |
| title | Positive solutions to second-order singular nonlocal problems: existence and sharp conditions |
| title_full | Positive solutions to second-order singular nonlocal problems: existence and sharp conditions |
| title_fullStr | Positive solutions to second-order singular nonlocal problems: existence and sharp conditions |
| title_full_unstemmed | Positive solutions to second-order singular nonlocal problems: existence and sharp conditions |
| title_short | Positive solutions to second-order singular nonlocal problems: existence and sharp conditions |
| title_sort | positive solutions to second order singular nonlocal problems existence and sharp conditions |
| topic | Sharp conditions Singular boundary value problems with integral boundary conditions Hölder’s inequality Fixed point theorems Positive solutions |
| url | http://link.springer.com/article/10.1186/s13661-019-1289-7 |
| work_keys_str_mv | AT shiqima positivesolutionstosecondordersingularnonlocalproblemsexistenceandsharpconditions AT xuemeizhang positivesolutionstosecondordersingularnonlocalproblemsexistenceandsharpconditions |