### Abstract

In this paper, we examine the solution set to the coupled system where λ, μ∈ R, x∈ [a, b], and the system (*) is subject to zero Dirichlet boundary data on u and v. We determine conditions on f and g which permit us to assert the existence of continua of solutions to (*) characterized by u having n−1 simple zeros in (a, b), v having m− 1 simple zeros in (a, b), where n and m are positive but not necessarily equal integers. Moreover, we also determine conditions under which these continua link solutions to (*) of the form (λ,μ, u, 0) with u having n− 1 simple zeros in (a, b) to solutions of (*) of the form (λ,μ, 0, v) with v having m−1 simple zeros in (a, b).

Original language | English (US) |
---|---|

Pages (from-to) | 633-644 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 107 |

Issue number | 3 |

DOIs | |

State | Published - 1989 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Global preservation of nodal structure in coupled systems of nonlinear sturm-liouville boundary value problems.** / Cantrell, Robert.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Global preservation of nodal structure in coupled systems of nonlinear sturm-liouville boundary value problems

AU - Cantrell, Robert

PY - 1989

Y1 - 1989

N2 - In this paper, we examine the solution set to the coupled system where λ, μ∈ R, x∈ [a, b], and the system (*) is subject to zero Dirichlet boundary data on u and v. We determine conditions on f and g which permit us to assert the existence of continua of solutions to (*) characterized by u having n−1 simple zeros in (a, b), v having m− 1 simple zeros in (a, b), where n and m are positive but not necessarily equal integers. Moreover, we also determine conditions under which these continua link solutions to (*) of the form (λ,μ, u, 0) with u having n− 1 simple zeros in (a, b) to solutions of (*) of the form (λ,μ, 0, v) with v having m−1 simple zeros in (a, b).

AB - In this paper, we examine the solution set to the coupled system where λ, μ∈ R, x∈ [a, b], and the system (*) is subject to zero Dirichlet boundary data on u and v. We determine conditions on f and g which permit us to assert the existence of continua of solutions to (*) characterized by u having n−1 simple zeros in (a, b), v having m− 1 simple zeros in (a, b), where n and m are positive but not necessarily equal integers. Moreover, we also determine conditions under which these continua link solutions to (*) of the form (λ,μ, u, 0) with u having n− 1 simple zeros in (a, b) to solutions of (*) of the form (λ,μ, 0, v) with v having m−1 simple zeros in (a, b).

UR - http://www.scopus.com/inward/record.url?scp=84966247811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966247811&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1989-0975633-X

DO - 10.1090/S0002-9939-1989-0975633-X

M3 - Article

VL - 107

SP - 633

EP - 644

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -