An existence result for nonlinear elliptic problems involving critical Sobolev exponent

Abstract

An existence result for nonlinear elliptic problems involving critical Sobolev exponent Annales de l'I. H. P., section C, tome 2, n o 6 (1985), p. 463-470 <http://www.numdam.org/item?id=AIHPC_1985__2_6_463_0> © Gauthier-Villars, 1985, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section C » (http://www.elsevier.com/locate/anihpc) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

An Existence Result for a Problem with Critical Growth and Lack of Strict Convexity

“…We aim to apply the linking theorem [9]. Since Again, this is proved in [4] in both cases (a) and (b) (in case (a), the condition N ≥ 5 needs to be required, see also [7,Corollary 1]) when Ψ(ξ) = 1 2 |ξ| 2 , but by (Ψ 3 ) the assertion is true also in our case. Finally, it is clear that J(u) ≤ 0 for every u ∈ E − .…”

The Brezis–Nirenberg problem for nonlocal systems

“…In 1985, Capozzi, Fortunato and Palmieri proved in [5] the existence of a nontrivial solution of (1.2) for all λ > 0 and N ≥ 5 or for N ≥ 4 and λ different from an eigenvalue of −∆. Let s ∈ (0, 1) and N > 2s.…”

Infinitely many solutions for quasilinear elliptic equations involving double critical terms and boundary geometry

“…For more existence results, we refer to e.g. [2,3,8,9,13,15,30] on semilinear problems and [6,11,12,14,16,20,21,26,34] on quasilinear problems.…”