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The main aim of this paper is to study and establish some new coincidence point and common fixed point theorems for solutions of the stationary Schrödinger equation on cones. An interesting application is to investigate the existence and uniqueness for solutions of the Dirichlet problem with respect to the Schrödinger operator on cones and the growth property of them.

RETRACTED ARTICLE: Fixed point theorems for solutions of the stationary Schrödinger equation on cones