Combined effects of the Hardy potential and lower order terms in fractional Laplacian equations
Abstract In this paper we consider the existence and regularity of solutions to the following nonlocal Dirichlet problems: {(−Δ)su−λu|x|2s+up=f(x),x∈Ω,u>0,x∈Ω,u=0,x∈RN∖Ω, $$ \textstyle\begin{cases} (-\Delta)^{s} u-\lambda\frac{u}{|x|^{2s}}+u^{p}=f(x), &x\in\Omega, \\ u>0, &x\in\Omega,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-04-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-0980-4 |
| Summary: | Abstract In this paper we consider the existence and regularity of solutions to the following nonlocal Dirichlet problems: {(−Δ)su−λu|x|2s+up=f(x),x∈Ω,u>0,x∈Ω,u=0,x∈RN∖Ω, $$ \textstyle\begin{cases} (-\Delta)^{s} u-\lambda\frac{u}{|x|^{2s}}+u^{p}=f(x), &x\in\Omega, \\ u>0, &x\in\Omega, \\ u=0, & x\in\mathbb{R}^{N}\setminus\Omega, \end{cases} $$ where (−Δ)s $(-\Delta)^{s}$ is the fractional Laplacian operator, s∈(0,1) $s\in(0,1)$, Ω⊂RN $\Omega\subset\mathbb{R}^{N}$ is a bounded domain with Lipschitz boundary such that 0∈Ω $0\in\Omega$, f is a nonnegative function that belongs to a suitable Lebesgue space. |
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| ISSN: | 1687-2770 |