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oai:docta.ucm.es:20.500.14352/338142023-08-26T20:16:27Zcom_20.500.14352_14col_20.500.14352_15

Asymptotic behavior of large radial solutions of a polyharmonic equation with superlinear growth Díaz Díaz, Jesús Ildefonso Lazzo, M. Schmidt, P.G. 517.9 Higher-order elliptic equations Polyharmonic equations Radial solutions Large solutions Boundary blow-up Asymptotic behavior Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias This paper concerns the blow-up behavior of large radial solutions of polyharmonic equations with power nonlinearities and positive radial weights. Specifically, we consider radially symmetric solutions of mu = c(|x|)|u| p on an annulus {x ∈ Rn | σ ≤ |x| < ρ}, with ρ ∈ (0,∞) and σ ∈ [0, ρ), that diverge to infinity as |x| → ρ. Here n,m ∈ N, p ∈ (1,∞), and c is a positive continuous function on the interval [σ, ρ]. Letting φρ(r) := QCρ/(ρ −r)q for r ∈ [σ, ρ), with q := 2m/(p−1), Q := (q(q +1)···(q +2m−1))1/(p−1), and Cρ := c(ρ)−1/(p−1), we show that, as |x| → ρ, the ratio u(x)/φρ(|x|) remains between positive constants that depend only on m and p. Extending well-known results for the second-order problem, we prove in the fourth-order case that u(x)/φρ(|x|) → 1 as |x| → ρ and obtain precise asymptotic expansions if c is sufficiently smooth at ρ. In certain higher-order cases, we find solutions for which the ratio u(x)/φρ(|x|)does not converge, but oscillates about 1 with non-vanishing amplitude. Unión Europea. FP7 DGISPI, Spain Research Group MOMAT, UCM MIUR, PRIN “Metodi variazionali e topologici ed equazioni differenziali nonlineari.” Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-19T13:28:36Z 2023-06-19T13:28:36Z 2014 journal article https://hdl.handle.net/20.500.14352/33814 0022-0396 10.1016/j.jde.2014.08.008 eng ITN FIRST (238702) MTM2011-26119 910480 restricted access application/pdf Elsevier