On a class of nonhomogeneous equations of Hénon-type : symmetry breaking and non radial solutions.

Abstract
In this work we study the following Hénon-type equation ⎧⎪⎨ ⎪⎩ −div ( |∇u|p−2∇u |x|ap ) = |x|βf(u), in B; u > 0, in B; u = 0, on ∂B; where B := { x ∈ RN ; |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 < Np+pβ 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.
Description
Keywords
Degenerate operator
Citation
ASSUNÇÃO, R. B. et al. On a class of nonhomogeneous equations of Hénon-type : symmetry breaking and non radial solutions. Nonlinear Analysis, v. 165, p. 102-120, dez. 2017. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0362546X17302420>. Acesso em: 16 jun. 2018.