On some nonlinear fractional equations involving the Bessel operator

Abstract

Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation ${\left(I-\Delta \right)}^{\alpha }u=\lambda b(x)|u{|}^{p-2}u+c(x)|u{|}^{q-2}u$ in ${\mathbb{R}}^N$. Our existence results are based on compact embedding properties for weighted spaces.

References in corpus (1)

• Nonlocal diffusion and applications