## Abstract

We consider the Dirichlet problem for a class of fully nonlinear elliptic equations on a bounded domain ω We assume that is symmetric about a hyperplane H and convex in the direction perpendicular to H. Each nonnegative solution of such a problem is symmetric about H and, if strictly positive, it is also decreasing in the direction orthogonal to H on each side of H. The latter is of course not true if the solution has a nontrivial nodal set. In this paper we prove that for a class of domains, including for example all domains which are convex (in all directions), there can be at most one nonnegative solution with a nontrivial nodal set. For general domains, there are at most nitely many such solutions.

Original language | English (US) |
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Pages (from-to) | 2657-2667 |

Number of pages | 11 |

Journal | Discrete and Continuous Dynamical Systems- Series A |

Volume | 34 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2014 |

## Keywords

- Multiplicity
- Nodal set
- Nonlinear elliptic equations
- Symmetry