### 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 sign-changing solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

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

Pages (from-to) | 1041-1053 |

Number of pages | 13 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 27 |

Issue number | 4 |

State | Published - Sep 1997 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Rocky Mountain Journal of Mathematics*,

*27*(4), 1041-1053.

**A sign-changing solution for a superlinear Dirichlet problem.** / Castro, Alfonso; Cossio, Jorge; Neuberger, John M.

Research output: Contribution to journal › Article

*Rocky Mountain Journal of Mathematics*, vol. 27, no. 4, pp. 1041-1053.

}

TY - JOUR

T1 - A sign-changing solution for a superlinear Dirichlet problem

AU - Castro, Alfonso

AU - Cossio, Jorge

AU - Neuberger, John M.

PY - 1997/9

Y1 - 1997/9

N2 - 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 sign-changing solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

AB - 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 sign-changing solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

KW - Deformation lemma

KW - Dirichlet problem

KW - Sign-changing solution

KW - Subcritical

KW - Superlinear

UR - http://www.scopus.com/inward/record.url?scp=0031372470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031372470&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031372470

VL - 27

SP - 1041

EP - 1053

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 4

ER -