Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems
We establish the existence and uniqueness of a positive solution to the following fourth-order value problem: u(4)(x)=a(x)uσ(x), x∈(0,1) with the boundary conditions u(0)=u(1)=u'(0)=u'(1)=0, where σ∈(-1,1) and a is a nonnegative continuous function on (0, 1) that may be singular at x=0 or...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/657926 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567270001344512 |
|---|---|
| author | Ramzi S. Alsaedi |
| author_facet | Ramzi S. Alsaedi |
| author_sort | Ramzi S. Alsaedi |
| collection | DOAJ |
| description | We establish the existence and uniqueness of a positive solution to the following fourth-order value problem: u(4)(x)=a(x)uσ(x), x∈(0,1) with the boundary conditions u(0)=u(1)=u'(0)=u'(1)=0, where σ∈(-1,1) and a is a nonnegative continuous function on (0, 1) that may be singular at x=0 or x=1. We also give the global behavior of such a solution. |
| format | Article |
| id | doaj-art-dbeb5b15cb7d47e88b1c1c2717b78a0a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dbeb5b15cb7d47e88b1c1c2717b78a0a2025-02-03T01:01:56ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/657926657926Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value ProblemsRamzi S. Alsaedi0Department of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh Campus, P.O. Box 344, Rabigh 21911, Saudi ArabiaWe establish the existence and uniqueness of a positive solution to the following fourth-order value problem: u(4)(x)=a(x)uσ(x), x∈(0,1) with the boundary conditions u(0)=u(1)=u'(0)=u'(1)=0, where σ∈(-1,1) and a is a nonnegative continuous function on (0, 1) that may be singular at x=0 or x=1. We also give the global behavior of such a solution.http://dx.doi.org/10.1155/2014/657926 |
| spellingShingle | Ramzi S. Alsaedi Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems Abstract and Applied Analysis |
| title | Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems |
| title_full | Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems |
| title_fullStr | Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems |
| title_full_unstemmed | Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems |
| title_short | Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems |
| title_sort | existence and global behavior of positive solutions for some fourth order boundary value problems |
| url | http://dx.doi.org/10.1155/2014/657926 |
| work_keys_str_mv | AT ramzisalsaedi existenceandglobalbehaviorofpositivesolutionsforsomefourthorderboundaryvalueproblems |