The upper and lower solution method for some fourth-order boundary value problems
In this paper, we are concerned with the fourth-order two-point boundary value problem u ( i v ) ( t ) = f ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) , u ‴ ( t ) ) , 0 < t < 1 , u ( 0 ) = u ′ ( 1 ) = u ″ ( 0 ) = u ‴ ( 1 ) = 0 . By placing certain restrictions on the nonlinear term f , we obtain the...
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| Published in | Nonlinear analysis Vol. 67; no. 6; pp. 1704 - 1709 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
15.09.2007
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0362-546X 1873-5215 |
| DOI | 10.1016/j.na.2006.08.009 |
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| Abstract | In this paper, we are concerned with the fourth-order two-point boundary value problem
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By placing certain restrictions on the nonlinear term
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, we obtain the existence results for the fourth-order two-point boundary value problem via the lower and upper solution method. In particular, a new truncating technique and an appropriate Nagumo-type condition are introduced and employed. |
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| AbstractList | In this paper, we are concerned with the fourth-order two-point boundary value problem
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By placing certain restrictions on the nonlinear term
f
, we obtain the existence results for the fourth-order two-point boundary value problem via the lower and upper solution method. In particular, a new truncating technique and an appropriate Nagumo-type condition are introduced and employed. In this paper, we are concerned with the fourth-order two-point boundary value problem |
| Author | Bai, Zhanbing |
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| Keywords | Fourth-order boundary value problem Lower and upper solutions 34B15 Integral–differential equation Nagumo-type condition Boundary value problem Differential equation Nonlinear analysis Integral equation Fourth-order boundary value problem; Lower and upper solutions; Nagumo-type condition; Integral-differential equation Mathematical model Multidisciplinary |
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| References | Schroder (b13) 1984; 8 Ehme, Eloe, Henderson (b9) 2001; 180 Ma, Zhang, Fu (b12) 1997; 215 Bai (b3) 2000; 248 Gupta (b10) 1988; 26 Cabada (b5) 1994; 185 Jiang, Gao, Wan (b11) 2002; 132 Usmani (b14) 1979; 77 Agarwal (b2) 1989; 2 Aftabizadeh (b1) 1986; 116 De Coster, Fabry, Munyamarere (b6) 1994; 17 Del Pino, Manasevich (b8) 1991; 112 Bai, Wang (b4) 2002; 270 De Coster, Sanchez (b7) 1994; 14 Schroder (10.1016/j.na.2006.08.009_b13) 1984; 8 Del Pino (10.1016/j.na.2006.08.009_b8) 1991; 112 Bai (10.1016/j.na.2006.08.009_b3) 2000; 248 Cabada (10.1016/j.na.2006.08.009_b5) 1994; 185 Agarwal (10.1016/j.na.2006.08.009_b2) 1989; 2 Jiang (10.1016/j.na.2006.08.009_b11) 2002; 132 Bai (10.1016/j.na.2006.08.009_b4) 2002; 270 Gupta (10.1016/j.na.2006.08.009_b10) 1988; 26 Ma (10.1016/j.na.2006.08.009_b12) 1997; 215 Ehme (10.1016/j.na.2006.08.009_b9) 2001; 180 De Coster (10.1016/j.na.2006.08.009_b6) 1994; 17 Aftabizadeh (10.1016/j.na.2006.08.009_b1) 1986; 116 Usmani (10.1016/j.na.2006.08.009_b14) 1979; 77 De Coster (10.1016/j.na.2006.08.009_b7) 1994; 14 |
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Appl. doi: 10.1006/jmaa.1997.5639 – volume: 26 start-page: 289 year: 1988 ident: 10.1016/j.na.2006.08.009_b10 article-title: Existence and uniqueness theorem for a bending of an elastic beam equation publication-title: Appl. Anal. doi: 10.1080/00036818808839715 – volume: 180 start-page: 51 year: 2001 ident: 10.1016/j.na.2006.08.009_b9 article-title: Upper and lower solution methods for fully nonlinear boundary value problems publication-title: J. Differential Equations doi: 10.1006/jdeq.2001.4056 |
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| SubjectTerms | Exact sciences and technology Fourth-order boundary value problem Integral equations Integral–differential equation Lower and upper solutions Mathematical analysis Mathematics Nagumo-type condition Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Partial differential equations, boundary value problems Sciences and techniques of general use |
| Title | The upper and lower solution method for some fourth-order boundary value problems |
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