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- W2749204522 abstract "In this paper we study the asymptotic and qualitative properties of least energy radial sign-changing solutions of the fractional Brezis--Nirenberg problem ruled by the s-laplacian, in a ball of $mathbb{R}^n$, when $s in (0,1)$ and $n > 6s$. As usual, $lambda$ is the (positive) parameter in the linear part in $u$, and we consider $lambda$ close to zero. We prove that if such solutions vanish at the center of the ball then they vanish everywhere, we establish a bound on the number of sign-changes and, when $s$ is close to $1$, for a suitable value of the parameter $lambda$ such solutions change sign exactly once. Moreover, for any $s in (0,1)$ and $lambda$ sufficiently small we prove that the number of connected components of the complement of the nodal set corresponds to the number of sign-changes plus one. In addition, for any $s in (frac{1}{2},1)$, we prove that least energy nodal solutions which change sign exactly once have the limit profile of a tower of bubbles, as $lambda to 0^+$, i.e. the positive and negative parts concentrate at the same point (which is the center of the ball) with different concentration speeds." @default.
- W2749204522 created "2017-08-31" @default.
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- W2749204522 date "2017-08-21" @default.
- W2749204522 modified "2023-09-27" @default.
- W2749204522 title "On the structure of the nodal set and asymptotics of least energy sign-changing radial solutions of the fractional Brezis-Nirenberg problem" @default.
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