A generalization of the well-known Hartman-Nagumo inequality to the case of the vector ordinary p-Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.
Mawhin, J., & Urena, A. (2002). A Hartman-Nagumo inequality for the vector ordinary p-Laplacian and applications to nonlinear boundary value problems. Journal of Inequalities and Applications, 7(5), 701-725. https://doi.org/10.1155/S102558340200036X (Original work published 2002)