### Abstract

This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem Δu + f(u) = h(x) + cφ(x) on the unit ball Ω ⊃ R^{N} with boundary condition u = 0 on ∂ω. Here 0(x) is a positive function and /(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f'(u) < n, where p, is the smallest positive eigenvalue for Δ1 + μ = 0 in ω with -0 on ∂ω. It is shown that, given any integer k > 0, the value c may be chosen so large that there are 2k + 1 solutions with k or less interior nodes. Existence of positive solutions is excluded for large enough values of c.

Original language | English (US) |
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Pages (from-to) | 1919-1945 |

Number of pages | 27 |

Journal | Transactions of the American Mathematical Society |

Volume | 351 |

Issue number | 5 |

DOIs | |

State | Published - 1999 |

### Keywords

- Critical exponent
- Dirichlet problem
- Nodal curves
- Radially symmetric
- Superlinear jumping nonlinearity

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

*Transactions of the American Mathematical Society*,

*351*(5), 1919-1945. https://doi.org/10.1090/s0002-9947-99-02110-8