A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian
Date
2003-10-21
Authors
Benalili, Mohamed
Youssef, Maliki
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We introduce a reduction method for proving the existence of solutions to elliptic equations involving the p-Laplacian operator. The existence of solutions is implied by the existence of a positive essentially weak subsolution on a manifold and the existence of a positive supersolution on each compact domain of this manifold. The existence and nonexistence of positive supersolutions is given by the sign of the first eigenvalue of a nonlinear operator.
Description
Keywords
Analysis on manifolds, Semi-linear elliptic PDE
Citation
Benalili, M., & Maliki, Y. (2003). A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian. <i>Electronic Journal of Differential Equations, 2003</i>(106), pp. 1-10.
Rights
Attribution 4.0 International