Uniform a priori estimates for positive solutions of higher order Lane-Emden equations in Rn

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Wei Dai
Beihang University (BUAA) (Beijing, Xina).School of Mathematical Sciences
Thomas Duyckaerts
Universit´e Sorbonne, Institut Galil´ee.

In this paper we study the existence of uniform a priori estimates for positive solutions to Navier problems of higher order Lane–Emden equations


(0.1)(−∆)mu(x) = u p (x), x ∈ Ω,


for all large exponents p, where Ω ⊂ Rn is a star-shaped or strictly convex bounded domain with C2m−2 boundary, n ≥ 4, and 2 ≤ m ≤ n 2 . Our results extend those of previous authors for second order m = 1 to general higher order cases m ≥ 2.

Paraules clau
uniform a priori estimates, higher order Lane–Emden equations, Navier problems, positive solutions, blow up

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Dai, Wei; Duyckaerts, Thomas. «Uniform a priori estimates for positive solutions of higher order Lane-Emden equations in Rn». Publicacions Matemàtiques, 2021, vol.VOL 65, núm. 1, p. 319–333, https://raco.cat/index.php/PublicacionsMatematiques/article/view/383990.
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