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

• Autores: Wei Dai, Thomas Duyckaerts
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 1, 2021, págs. 319-333
• Idioma: inglés
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• Resumen

  • 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.