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- W2808065498 abstract "In this article, we show the global multiplicity result for the following nonlocal singular problem begin{equation*} (P_la):;quad (-De)^s u = u^{-q} + la u^{{2^*_s}-1}, quad u>0 ; text{in}; Om,quad u = 0 ; mbox{in}; mb R^n setminusOm, end{equation*} where $Om$ is a bounded domain in $mb{R}^n$ with smooth boundary $partial Om$, $n > 2s,; s in (0,1),; la >0,; q>0$ satisfies $q(2s-1)<(2s+1)$ and $2^*_s=frac{2n}{n-2s}$. Employing the variational method, we show the existence of at least two distinct weak positive solutions for $(P_la)$ in $X_0$ when $la in (0,La)$ and no solution when $la>La$, where $La>0$ is appropriately chosen. We also prove a result of independent interest that any weak solution to $(P_lambda)$ is in $C^alpha(R^n)$ with $alpha=alpha(s,q)in (0,1)$. The asymptotic behaviour of weak solutions reveals that this result is sharp." @default.
- W2808065498 created "2018-06-21" @default.
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- W2808065498 date "2019-01-01" @default.
- W2808065498 modified "2023-09-27" @default.
- W2808065498 title "A Global multiplicity result for a very singular critical nonlocal equation" @default.
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