Abstract

PARDO, Rosa. On the existence of a priori bounds for positive solutions of elliptic problems, II. Integración - UIS [online]. 2019, vol.37, n.1, pp.113-148. ISSN 0120-419X.  https://doi.org/10.18273/revint.v37n1-2019006..

We continue studying the existence of uniform L°° a priori bounds for positive solutions of subcritical elliptic equations We provide sufficient conditions for having a-priori L ∞ bounds for positive solutions to a class of subcritical elliptic problems in bounded, convex, C2 domains. In this part II, we extend our results to Hamiltonian elliptic systems -Δu = f(v), -Δv = g(u), in Ω, u = v = 0 on when with α, β > 2/(N - 2), and p,q are lying in the critical Sobolev hyperbolae For quasilinear elliptic equations involving the p-Laplacian, there exists a-priori bounds for positive solutions of with p* = Np/(N - p), and α > p/(N - p). We also study the asymptotic behavior of radially symmetric solutions u α = u α (r) of (P)2 as α → 0.

MSC2010: 35B45, 35J92, 35B33, 35J47, 35J60, 35J61.

Keywords : A priori estimates; subcritical nonlinearity; moving planes method; Pohozaev identity; critical Sobolev hyperbola; biparameter bifurcation.

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