## Differential and Integral Equations

### On positive solutions of quasilinear elliptic equations

#### Abstract

In 1981, Peter Hess established a multiplicity result for solutions of boundary-value problems for nonlinear perturbations of the Laplace operator. The sufficient conditions given were later shown to be also necessary by Dancer and the second author. In this paper, we show that similar (and slightly more general) results hold when the Laplace operator is replaced by the $p-$Laplacian. Some applications to singular problems are given, as well.

#### Article information

Source
Differential Integral Equations Volume 22, Number 9/10 (2009), 829-842.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019510

Mathematical Reviews number (MathSciNet)
MR2553058

Zentralblatt MATH identifier
1240.35210

Subjects
Primary: 35J92: Quasilinear elliptic equations with p-Laplacian
Secondary: 35B45: A priori estimates

#### Citation

Loc, Nguyen Hoang; Schmitt, Klaus. On positive solutions of quasilinear elliptic equations. Differential Integral Equations 22 (2009), no. 9/10, 829--842. https://projecteuclid.org/euclid.die/1356019510.