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We show the existence of nonconstant bounded p-harmonic functions on Cartan-Hadamard manifolds of pinched negative curvature by solving the asymptotic Dirichlet problem at infinity for the p-Laplacian. More precisely, we prove that given a continuous function h on the sphere at infinity there exists a unique p-harmonic function u on M with boundary values h.

Asymptotic Dirichlet problem for the $p$-Laplacian on Cartan-Hadamard manifolds