### 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 C^{1} 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 |
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Pages (from-to) | 17-22 |

Number of pages | 6 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 292 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Apr 2004 |

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### Keywords

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

### Cite this

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*Journal of Mathematical Analysis and Applications*, vol. 292, no. 1, pp. 17-22. https://doi.org/10.1016/j.jmaa.2003.08.043

**Solution curves and exact multiplicity results for 2mth order boundary value problems.** / Bari, Rehana; Rynne, Bryan P.

Research output: Contribution to journal › Article

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

UR - http://www.scopus.com/inward/record.url?scp=1842502707&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2003.08.043

DO - 10.1016/j.jmaa.2003.08.043

M3 - Article

VL - 292

SP - 17

EP - 22

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -