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The existence of a nontrivial solution in some ‘weaker’ sense of the system of equations:is proved. Here,,,,  l ,  w  are bounded, nonnegative real-valued functions in Ω,  μ  is a nonnegative Radon measure and  k &gt;1 belongs to a certain range.

Existence of solution for a system involving a singular-nonlocal operator, a singularity and a Radon measure