## Differential and Integral Equations

### On maximum principles and existence of positive solutions for some cooperative elliptic systems

#### Abstract

In this paper, we provide alternative simple proofs for some of the results in [12], with applications to nonlinear systems, and an extension of the necessary and sufficient condition for the Maximum Principle to some cooperative quasi-linear elliptic systems involving the $p$-Laplacian. We also show that under the same conditions, we have existence of positive solutions.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 1 (1995), 69-85.

Dates
First available in Project Euclid: 21 May 2013

https://projecteuclid.org/euclid.die/1369143784

Mathematical Reviews number (MathSciNet)
MR1296110

Zentralblatt MATH identifier
0821.35018

Subjects
Primary: 35J45
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B50: Maximum principles

#### Citation

Fleckinger, J.; Hernández, J.; de Thélin, F. On maximum principles and existence of positive solutions for some cooperative elliptic systems. Differential Integral Equations 8 (1995), no. 1, 69--85. https://projecteuclid.org/euclid.die/1369143784