### Abstract

We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

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

Pages (from-to) | 3657-3662 |

Number of pages | 6 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 30 |

Issue number | 6 |

State | Published - Dec 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Multiplicity of solutions
- Nonlinear Dirichlet problem

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Analysis, Theory, Methods and Applications*,

*30*(6), 3657-3662.

**On multiple solutions of a nonlinear Dirichlet problem.** / Castro, Alfonso; Cossio, Jorge; Neuberger, John M.

Research output: Contribution to journal › Article

*Nonlinear Analysis, Theory, Methods and Applications*, vol. 30, no. 6, pp. 3657-3662.

}

TY - JOUR

T1 - On multiple solutions of a nonlinear Dirichlet problem

AU - Castro, Alfonso

AU - Cossio, Jorge

AU - Neuberger, John M

PY - 1997/12

Y1 - 1997/12

N2 - We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

AB - We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

KW - Multiplicity of solutions

KW - Nonlinear Dirichlet problem

UR - http://www.scopus.com/inward/record.url?scp=0001130594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001130594&partnerID=8YFLogxK

M3 - Article

VL - 30

SP - 3657

EP - 3662

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 6

ER -