Revista Matemática Iberoamericana


Full-Text PDF (342 KB) | Metadata | Table of Contents | RMI summary
Volume 35, Issue 6, 2019, pp. 1859–1884
DOI: 10.4171/rmi/1104

Published online: 2019-08-05

A Berestycki–Lions type result and applications

Claudianor O. Alves[1], Ronaldo C. Duarte[2] and Marco A.S. Souto[3]

(1) Universidade Federal de Campina Grande, Brazil
(2) Universidade do Estado do Rio Grande do Norte, Mossoró, Brazil
(3) Universidade Federal de Campina Grande, Brazil

In this paper we show an abstract theorem about the existence of critical points for a functional $I$, which permits us to prove the existence of solutions for a large class of Berestycki–Lions type problems. In the proof of the abstract result we apply the deformation lemma on a special set associated with $I$ called Pohozaev set.

Keywords: Nonlinear elliptic equations, variational methods, nonsmooth analysis

Alves Claudianor, Duarte Ronaldo, Souto Marco: A Berestycki–Lions type result and applications. Rev. Mat. Iberoam. 35 (2019), 1859-1884. doi: 10.4171/rmi/1104