Abstract
The main goal of this paper is to formulate sufficient conditions guaranteeing the existence of decaying solutions of the system of elliptic equations in a certain exterior domain. The asymptotic behavior of these solutions and their gradients will be characterized. We focus on the construction of uncountable sets of nondecreasing sequences of minimal solutions with finite energy in a neighborhood of infinity. Our method can be applied for nonlinearities which are negative at the origin (semipositone problem).
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