Entire nodal solutions to the pure critical exponent problem arising from concentration

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• 作者：Mó ; nica Clapp ^{monica.clapp@im.unam.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 35B08 ; 35B33 ; 35B40 ; secondary ; 35J20 ; 35J25 ; 35J61
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：261
• 期：6
• 页码：3042-3060
• 全文大小：327 K

文摘

We obtain new sign changing solutions to the problem for N≥4$N\ge 4$ where $2^{⁎}:=\frac{2N}{N-2}$ is the critical Sobolev exponent. These solutions arise as asymptotic profiles of sign changing solutions to the problem in some bounded smooth domains Ω in R^N${\mathbb{R}}^N$ for p∈(2,2^⁎)$p\in (2,2^{⁎})$ as p→2^⁎$p\to 2^{⁎}$.

We exhibit solutions u_p$u_p$ to (℘_p)$({\wp }_p)$ which blow up at a single point as p→2^⁎$p\to 2^{⁎}$, developing a peak whose asymptotic profile is a rescaling of a nonradial sign changing solution to problem (℘_∞)$({\wp }_{\infty })$.

We also obtain existence and multiplicity of sign changing nonradial solutions to the Bahri–Coron problem (℘_2^⁎)$({\wp }_{2^{⁎}})$ in annuli.