Differential and Integral Equations
- Differential Integral Equations
- Volume 22, Number 9/10 (2009), 829-842.
On positive solutions of quasilinear elliptic equations
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.
Differential Integral Equations Volume 22, Number 9/10 (2009), 829-842.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J92: Quasilinear elliptic equations with p-Laplacian
Secondary: 35B45: A priori estimates
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.