In this paper, we establish several new existence theorems for positive solutions of systems of (2n,2m) $(2n,2m)$-order of two p-Laplacian equations. The results are based on the Krasnosel’skii fixed point theorem and mainly complement those of Djebali, Moussaoui, and Precup.
A parabolic equation related to the p-Laplacian is considered. If the equation is degenerate on the boundary, then demonstrating the regularity on the boundary is difficult, the trace on the boundary cannot be defined, in general. The existence and uniqueness of weak solutions are researched. Based on uniqueness, the stability of solutions can be proved without any boundary condition.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.