### Abstract

We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12]

Original language | English (US) |
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Pages (from-to) | 1041-1053 |

Number of pages | 13 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 27 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1997 |

### Keywords

- Deformation lemma
- Dirichlet problem
- Sign-changing solution
- Subcritical
- Superlinear

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Castro, A., Cossio, J., & Neuberger, J. M. (1997). A sign-changing solution for a superlinear dirichlet problem.

*Rocky Mountain Journal of Mathematics*,*27*(4), 1041-1053. https://doi.org/10.1216/rmjm/1181071858