Multiple solutions for a class of fractional quasi-linear equations with critical exponential growth in ℝN

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This paper deals with a class of non-local equations involving the fractional p-Laplacian, where the non-linear term is assumed to have critical exponential growth. More specifically, by applying variational methods together with a suitable Trudinger-Moser inequality for fractional Sobolev space, we obtain the existence of at least two positive weak solutions.