### Abstract

The equation L// lambda u equals lambda F( lambda , u), u(0) equals u(1) equals 0, is studied, where L// lambda is a Sturm-Liouville operator depending on the parameter lambda , and F is some nonlinear operator. Results are obtained covering the existence of continua of positive solutions ( lambda , u). By imposing various growth conditions on F, results are obtained about the behavior of these continua for large and small values of lambda and the norm of u.

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

Pages (from-to) | 179-190 |

Number of pages | 12 |

Journal | Indiana University Mathematics Journal |

Volume | 25 |

Issue number | 2 |

State | Published - Feb 1976 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indiana University Mathematics Journal*,

*25*(2), 179-190.

**NONLINEAR ORDINARY AND FUNCTIONAL STURM-LIOUVILLE PROBLEMS.** / Kuiper, H. J.; Derrick, W. R.

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 25, no. 2, pp. 179-190.

}

TY - JOUR

T1 - NONLINEAR ORDINARY AND FUNCTIONAL STURM-LIOUVILLE PROBLEMS.

AU - Kuiper, H. J.

AU - Derrick, W. R.

PY - 1976/2

Y1 - 1976/2

N2 - The equation L// lambda u equals lambda F( lambda , u), u(0) equals u(1) equals 0, is studied, where L// lambda is a Sturm-Liouville operator depending on the parameter lambda , and F is some nonlinear operator. Results are obtained covering the existence of continua of positive solutions ( lambda , u). By imposing various growth conditions on F, results are obtained about the behavior of these continua for large and small values of lambda and the norm of u.

AB - The equation L// lambda u equals lambda F( lambda , u), u(0) equals u(1) equals 0, is studied, where L// lambda is a Sturm-Liouville operator depending on the parameter lambda , and F is some nonlinear operator. Results are obtained covering the existence of continua of positive solutions ( lambda , u). By imposing various growth conditions on F, results are obtained about the behavior of these continua for large and small values of lambda and the norm of u.

UR - http://www.scopus.com/inward/record.url?scp=0016919326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016919326&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0016919326

VL - 25

SP - 179

EP - 190

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 2

ER -