Key points are not available for this paper at this time.
This paper deals with the following nonlocal system of equations: \aligned \;in\;R^{d, \\ \;in\;R^d, \\ & u, \, v >0\, in \, R^d, aligned. (S) where 0sp, , >1, + = dpd-sp, and f, g are nontrivial nonnegative functionals in the dual space of D^s, p (R^d), i. e. , f, g 0, and (₃^ₒ, ) 'f, u₃^ₒ, 0, \, (₃^ₒ, ) 'g, u₃^ₒ, 0, whenever u is a nonnegative function in D^s, p (R^d). The primary objective of this paper is to present a global compactness result that offers a complete characterization of the Palais-Smale sequences of the energy functional associated with (S). Using this characterization, within a certain range of s, we establish the existence of a solution with negative energy for (S) when (f) = (g).
Biswas et al. (Fri,) studied this question.