In this paper we prove an existence result to the problem −∆u = |u| p−1 u in Ω, u =0 on ∂Ω, where Ω is a bounded domain in R N which is a perturbation of the annulus. Then there exists a sequence p 1 < p 2 < .. with lim p k = +∞ such that for any real k→+∞ number p > 1 and p 6 = p k there exist at least one solution with m nodal zones. In doing so, we also investigate the radial nodal solution in an annulus: we provide an estimate of its Morse index and analyze the asymptotic behavior as p → 1.
NODAL SOLUTIONS FOR LANE-EMDEN PROBLEMS IN ALMOST-ANNULAR DOMAINS
AMADORI, Anna Lisa;
2018-01-01
Abstract
In this paper we prove an existence result to the problem −∆u = |u| p−1 u in Ω, u =0 on ∂Ω, where Ω is a bounded domain in R N which is a perturbation of the annulus. Then there exists a sequence p 1 < p 2 < .. with lim p k = +∞ such that for any real k→+∞ number p > 1 and p 6 = p k there exist at least one solution with m nodal zones. In doing so, we also investigate the radial nodal solution in an annulus: we provide an estimate of its Morse index and analyze the asymptotic behavior as p → 1.File in questo prodotto:
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