Abstract

In this paper we investigate the monotonicity of solutions for the system involving the physically pseudo-relativistic Schrödinger operators by the sliding method. We first obtain the key ingredients needed in the sliding method either in bounded or unbounded domains, such as narrow region principles and maximum principles. Then we employ the direct sliding method to obtain monotonicity of solutions to several systems involving the pseudo-relativistic Schrödinger operators in bounded or unbounded domains with certain geometrical structures.

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