Existence of solutions for some higher order boundary value problems
In this paper, we are concerned with the existence of solutions for the higher order boundary value problem in the formu(2 m + 2) (x) = f (x, u (x), u″ (x), ..., u(2 m) (x)), x ∈ (0, 1),u(2 i) (0) = u(2 i) (1) = 0, 0 ≤ i ≤ m, where m is a given positive integer and f : [0, 1] × Rm + 1 → R is continu...
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th-cmuir.6653943832-52572014-08-30T02:56:19Z Existence of solutions for some higher order boundary value problems Charkrit S. Kananthai A. In this paper, we are concerned with the existence of solutions for the higher order boundary value problem in the formu(2 m + 2) (x) = f (x, u (x), u″ (x), ..., u(2 m) (x)), x ∈ (0, 1),u(2 i) (0) = u(2 i) (1) = 0, 0 ≤ i ≤ m, where m is a given positive integer and f : [0, 1] × Rm + 1 → R is continuous. We introduce a new maximum principle of higher order equations and develop a monotone method in the presence of lower and upper solutions for this problem. © 2006 Elsevier Inc. All rights reserved. 2014-08-30T02:56:19Z 2014-08-30T02:56:19Z 2007 Article 0022247X 10.1016/j.jmaa.2006.06.092 http://www.scopus.com/inward/record.url?eid=2-s2.0-33846625267&partnerID=40&md5=8dc9544e4bf347577cfe4204b6fd0466 http://cmuir.cmu.ac.th/handle/6653943832/5257 English |
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In this paper, we are concerned with the existence of solutions for the higher order boundary value problem in the formu(2 m + 2) (x) = f (x, u (x), u″ (x), ..., u(2 m) (x)), x ∈ (0, 1),u(2 i) (0) = u(2 i) (1) = 0, 0 ≤ i ≤ m, where m is a given positive integer and f : [0, 1] × Rm + 1 → R is continuous. We introduce a new maximum principle of higher order equations and develop a monotone method in the presence of lower and upper solutions for this problem. © 2006 Elsevier Inc. All rights reserved. |
| format |
Article |
| author |
Charkrit S. Kananthai A. |
| spellingShingle |
Charkrit S. Kananthai A. Existence of solutions for some higher order boundary value problems |
| author_facet |
Charkrit S. Kananthai A. |
| author_sort |
Charkrit S. |
| title |
Existence of solutions for some higher order boundary value problems |
| title_short |
Existence of solutions for some higher order boundary value problems |
| title_full |
Existence of solutions for some higher order boundary value problems |
| title_fullStr |
Existence of solutions for some higher order boundary value problems |
| title_full_unstemmed |
Existence of solutions for some higher order boundary value problems |
| title_sort |
existence of solutions for some higher order boundary value problems |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-33846625267&partnerID=40&md5=8dc9544e4bf347577cfe4204b6fd0466 http://cmuir.cmu.ac.th/handle/6653943832/5257 |
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1681420391028883456 |