Existence of solutions for perturbed fractional equations with two competing weighted nonlinear terms

This paper deals with a perturbed nonlocal equation of fractional Laplacian type involving two competing nonlinear terms with weights f and h . Under two kinds of integrability conditions on the ratio of f to h , we show some different existence results in this setting by using variational methods. Our results are extension of some problems studied by Carboni and Mugnai (J. Differ. Equ. 262(3):2393–2413, 2017 ) and Xiang et al. (J. Differ. Equ. 260(2):1392–1413, 2016 ).