Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives
We study the existence of monotone positive solutions for the semipositone right focal boundary value problems ⎧⎪⎪⎨ ⎪⎪⎩ (−1)(n−k)u(n)(t) = λf(t, u(t), u (t), . . . , u(k−1)(t)), t∈ (0, 1), u(i)(0) = 0, 0 ≤ i ≤ k − 1, u(j)(1) = 0, k≤ j ≤ n − 1, where λ > 0 is a parameter, n ≥ 3, 1 < k...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
Kexue Chubanshe
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/49496 |
| _version_ | 1848758251584225280 |
|---|---|
| author | Hao, X. Liu, L. Wu, Yong Hong |
| author_facet | Hao, X. Liu, L. Wu, Yong Hong |
| author_sort | Hao, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We study the existence of monotone positive solutions for the semipositone
right focal boundary value problems
⎧⎪⎪⎨
⎪⎪⎩
(−1)(n−k)u(n)(t) = λf(t, u(t), u
(t), . . . , u(k−1)(t)), t∈ (0, 1),
u(i)(0) = 0, 0 ≤ i ≤ k − 1,
u(j)(1) = 0, k≤ j ≤ n − 1,
where λ > 0 is a parameter, n ≥ 3, 1 < k ≤ n − 1 is fixed, f may change sign for
0 < t < 1 and we allow f is both semipositone and lower unbounded. Without making
any monotone type assumption, the existence results of at least one and two monotone positive solutions are obtained by means of the fixed point theorems in cones. |
| first_indexed | 2025-11-14T09:41:01Z |
| format | Journal Article |
| id | curtin-20.500.11937-49496 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:41:01Z |
| publishDate | 2012 |
| publisher | Kexue Chubanshe |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-494962017-08-04T07:08:03Z Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives Hao, X. Liu, L. Wu, Yong Hong We study the existence of monotone positive solutions for the semipositone right focal boundary value problems ⎧⎪⎪⎨ ⎪⎪⎩ (−1)(n−k)u(n)(t) = λf(t, u(t), u (t), . . . , u(k−1)(t)), t∈ (0, 1), u(i)(0) = 0, 0 ≤ i ≤ k − 1, u(j)(1) = 0, k≤ j ≤ n − 1, where λ > 0 is a parameter, n ≥ 3, 1 < k ≤ n − 1 is fixed, f may change sign for 0 < t < 1 and we allow f is both semipositone and lower unbounded. Without making any monotone type assumption, the existence results of at least one and two monotone positive solutions are obtained by means of the fixed point theorems in cones. 2012 Journal Article http://hdl.handle.net/20.500.11937/49496 Kexue Chubanshe restricted |
| spellingShingle | Hao, X. Liu, L. Wu, Yong Hong Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives |
| title | Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives |
| title_full | Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives |
| title_fullStr | Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives |
| title_full_unstemmed | Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives |
| title_short | Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives |
| title_sort | existence of monotone positive solutions for semipositone right focal boundary value problems with dependence on the derivatives |
| url | http://hdl.handle.net/20.500.11937/49496 |