Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem
The existence results of positive solutions are obtained for the fourth-order periodic boundary value problem u(4)−βu′′+αu=f(t,u,u′′), 0≤t≤1, u(i)(0)=u(i)(1), i=0,1,2,3, where f:[0,1]×R+×R→R+ is continuous, α,β∈R, and satisfy 0<α<((β/2)+2π2)2, β>−2π2,(α/π4)+(β/π2)+1>0. The discussion...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/826451 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849306853695029248 |
|---|---|
| author | Yongxiang Li |
| author_facet | Yongxiang Li |
| author_sort | Yongxiang Li |
| collection | DOAJ |
| description | The existence results of positive solutions are obtained for the fourth-order periodic boundary value problem u(4)−βu′′+αu=f(t,u,u′′), 0≤t≤1, u(i)(0)=u(i)(1), i=0,1,2,3, where f:[0,1]×R+×R→R+ is continuous, α,β∈R, and satisfy 0<α<((β/2)+2π2)2, β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones. |
| format | Article |
| id | doaj-art-1ed4f1321efb46b5bc529470eca92b2e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1ed4f1321efb46b5bc529470eca92b2e2025-08-20T03:54:57ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/826451826451Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value ProblemYongxiang Li0Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaThe existence results of positive solutions are obtained for the fourth-order periodic boundary value problem u(4)−βu′′+αu=f(t,u,u′′), 0≤t≤1, u(i)(0)=u(i)(1), i=0,1,2,3, where f:[0,1]×R+×R→R+ is continuous, α,β∈R, and satisfy 0<α<((β/2)+2π2)2, β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones.http://dx.doi.org/10.1155/2011/826451 |
| spellingShingle | Yongxiang Li Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem Abstract and Applied Analysis |
| title | Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem |
| title_full | Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem |
| title_fullStr | Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem |
| title_full_unstemmed | Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem |
| title_short | Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem |
| title_sort | existence of positive solutions for a fourth order periodic boundary value problem |
| url | http://dx.doi.org/10.1155/2011/826451 |
| work_keys_str_mv | AT yongxiangli existenceofpositivesolutionsforafourthorderperiodicboundaryvalueproblem |