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- W3105526458 abstract "We consider the semilinear Lane–Emden problem $$begin{aligned} left{ begin{array}{l@{quad }l}-Delta u= |u|^{p-1}u&{}quad text{ in }quad Omega u=0&{}quad text{ on }quad partial Omega end{array}right. quad (mathcal E_p) end{aligned}$$ where $$p>1$$ and $$Omega $$ is a smooth bounded symmetric domain of $${mathbb {R}}^2$$ . We show that for families $$(u_p)$$ of sign-changing symmetric solutions of $$(mathcal E_p)$$ an upper bound on their Morse index implies concentration of the positive and negative part, $$u_p^pm $$ , at the same point, as $$prightarrow +infty $$ . Then, an asymptotic analysis of $$u_p^+$$ and $$u_p^-$$ shows that the asymptotic profile of $$(u_p)$$ , as $$prightarrow +infty $$ , is that of a tower of two different bubbles." @default.
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- W3105526458 date "2014-11-23" @default.
- W3105526458 modified "2023-10-04" @default.
- W3105526458 title "Morse index and sign-changing bubble towers for Lane–Emden problems" @default.
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- W3105526458 doi "https://doi.org/10.1007/s10231-014-0467-6" @default.
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