### Abstract

Consider a system of weakly coupled elliptic partial differential equations where each equation in the system involves the same uniformly elliptic operator. We introduce several transformations which change the system into a system for which the classical extremum principle holds. This leads to pointwise comparison results of the component functions and, under additional assumptions, to positive solutions of the Dirichlet problem for the system.

Original language | English (US) |
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Pages (from-to) | 555-562 |

Number of pages | 8 |

Journal | Differential and Integral Equations |

Volume | 4 |

Issue number | 3 |

State | Published - 1991 |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Cosner, G., Schaefer, P. W., & Schmitt, K. (1991). Some comparison principles for weakly coupled systems of elliptic equations.

*Differential and Integral Equations*,*4*(3), 555-562.