RT Journal Article
T1 Asymptotic behavior of large radial solutions of a polyharmonic equation with superlinear growth
A1 Díaz Díaz, Jesús Ildefonso
A1 Lazzo, M.
A1 Schmidt, P.G.
AB 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.
PB Elsevier
SN 0022-0396
YR 2014
FD 2014
LK https://hdl.handle.net/20.500.14352/33814
UL https://hdl.handle.net/20.500.14352/33814
LA eng
NO Unión Europea. FP7
NO DGISPI, Spain
NO Research Group MOMAT, UCM
NO MIUR, PRIN “Metodi variazionali e topologici ed equazioni differenziali nonlineari.”
DS Docta Complutense
RD 19 abr 2025