On the Existence of a Non-trivial Non-negative Global Radial Weak Solution to a Fractional Laplacian Problem with a Singular Potential
Volume 64 / 2016
Bulletin Polish Acad. Sci. Math. 64 (2016), 175-183
MSC: Primary 35R11; Secondary 35B25.
DOI: 10.4064/ba8070-9-2016
Published online: 10 October 2016
Abstract
We prove the existence of a non-trivial non-negative radial weak solution to the problem Here N \gt 2\alpha , \alpha \in ({1}/{2},1), 1 \lt r \lt p \lt \frac{N+2\alpha}{N-2\alpha} and \mu \in \mathbb{R}. We also assume that b \gt 0 and 0 \lt \lambda \lt 4^\alpha \frac{\Gamma^2(\frac{N+2\alpha}4)}{\Gamma^2(\frac{N-2\alpha}4)}.
