On Some Nonlinear Fractional Equations Involving the Bessel Operator

Under different assumptions on the potential functions b and c, we study the fractional equation I-Δαu=λb(x)|u|p-2u+c(x)|u|q-2u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( I-\varDelta \right) ^{\alpha } u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$$\end{document} in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^N$$\end{document}. Our existence results are based on compact embedding properties for weighted spaces.