A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian
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.
Citation
Benalili, M., & Maliki, Y. (2003). A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian. Electronic Journal of Differential Equations, 2003(106), pp. 1-10.Rights License

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