# Solution curves and exact multiplicity results for 2mth order boundary value problems

Rehana Bari, Bryan P. Rynne

Research output: Contribution to journalArticle

### Abstract

For any integer m = 2, we consider the 2mth order boundary value problem (-1)m u(2m) (x) = ?g(u(x))u(x), x ? (-1, 1), u(i) (-1) = u(i) (1) = 0, i = 0,..., m - 1, where ? ? R, and the function g: R ? R is C1 and satisfies g(0) > 0, ±g' (?) > 0, ±? > 0, together with some further conditions as ? ? 8. We obtain curves of nontrivial solutions of this problem, bifurcating from u = 0 at the eigenvalues of the linearised problem, and obtain the exact number of solutions of the problem for ? lying in various intervals in R. © 2003 Elsevier Inc. All rights reserved.

Original language English 17-22 6 Journal of Mathematical Analysis and Applications 292 1 https://doi.org/10.1016/j.jmaa.2003.08.043 Published - 1 Apr 2004

### Fingerprint

Exact multiplicity
Multiplicity Results
Exact Results
Boundary Value Problem
Curve
Number of Solutions
G-function
Nontrivial Solution
Eigenvalue
Interval
Integer

### Keywords

• Exact multiplicity
• Nonlinear boundary value problems
• Ordinary differential equations

### Cite this

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title = "Solution curves and exact multiplicity results for 2mth order boundary value problems",
abstract = "For any integer m = 2, we consider the 2mth order boundary value problem (-1)m u(2m) (x) = ?g(u(x))u(x), x ? (-1, 1), u(i) (-1) = u(i) (1) = 0, i = 0,..., m - 1, where ? ? R, and the function g: R ? R is C1 and satisfies g(0) > 0, ±g' (?) > 0, ±? > 0, together with some further conditions as ? ? 8. We obtain curves of nontrivial solutions of this problem, bifurcating from u = 0 at the eigenvalues of the linearised problem, and obtain the exact number of solutions of the problem for ? lying in various intervals in R. {\circledC} 2003 Elsevier Inc. All rights reserved.",
keywords = "Exact multiplicity, Nonlinear boundary value problems, Ordinary differential equations",
author = "Rehana Bari and Rynne, {Bryan P.}",
year = "2004",
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day = "1",
doi = "10.1016/j.jmaa.2003.08.043",
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In: Journal of Mathematical Analysis and Applications, Vol. 292, No. 1, 01.04.2004, p. 17-22.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Solution curves and exact multiplicity results for 2mth order boundary value problems

AU - Bari, Rehana

AU - Rynne, Bryan P.

PY - 2004/4/1

Y1 - 2004/4/1

N2 - For any integer m = 2, we consider the 2mth order boundary value problem (-1)m u(2m) (x) = ?g(u(x))u(x), x ? (-1, 1), u(i) (-1) = u(i) (1) = 0, i = 0,..., m - 1, where ? ? R, and the function g: R ? R is C1 and satisfies g(0) > 0, ±g' (?) > 0, ±? > 0, together with some further conditions as ? ? 8. We obtain curves of nontrivial solutions of this problem, bifurcating from u = 0 at the eigenvalues of the linearised problem, and obtain the exact number of solutions of the problem for ? lying in various intervals in R. © 2003 Elsevier Inc. All rights reserved.

AB - For any integer m = 2, we consider the 2mth order boundary value problem (-1)m u(2m) (x) = ?g(u(x))u(x), x ? (-1, 1), u(i) (-1) = u(i) (1) = 0, i = 0,..., m - 1, where ? ? R, and the function g: R ? R is C1 and satisfies g(0) > 0, ±g' (?) > 0, ±? > 0, together with some further conditions as ? ? 8. We obtain curves of nontrivial solutions of this problem, bifurcating from u = 0 at the eigenvalues of the linearised problem, and obtain the exact number of solutions of the problem for ? lying in various intervals in R. © 2003 Elsevier Inc. All rights reserved.

KW - Exact multiplicity

KW - Nonlinear boundary value problems

KW - Ordinary differential equations

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JF - Journal of Mathematical Analysis and Applications

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