On a class of nonhomogeneous equations of Hénon-type: Symmetry breaking and non radial solutions. (December 2017)

• Record Type: Journal Article
• Authors: Assunção, Ronaldo Brasileiro; Miyagaki, Olimpio Hiroshi; de Assis Pereira, Gilberto; Rodrigues, Bruno Mendes
• Is Part Of: Nonlinear analysis. Volume 165(2017)
• Page Start: 102
• Page End: 120
• Publication Date: 2017-12
• Subjects: 35B07 -- 35J20 -- 35J60 -- 35J70; Hénon equation -- Degenerate operator -- Non radial solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.09.015
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work we study the following Hénon-type equation − div ∇ u p − 2 ∇ u x a p = x β f ( u ), in B ; u > 0, in B ; u = 0, on ∂ B ; where B ≔ x ∈ R N ; x < 1 is a ball centered at the origin, the parameters verify the inequalities 0 ≤ a < N − p p, N ≥ 4, β > 0, 2 ≤ p < N p + p β N − p ( a + 1 ), and the nonlinearity f is nonhomogeneous. By minimization on the Nehari manifold, we prove that for large values of the parameter β there is a symmetry breaking and non radial solutions appear.