Benalili, MohamedYoussef, Maliki2021-01-272021-01-272003-10-21Benalili, 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. 1-10.1072-6691https://hdl.handle.net/10877/13157We 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.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalAnalysis on manifoldsSemi-linear elliptic PDEArticle