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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).

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