Abstract
We show the variational structure of a multiplicity result of positive solutions u ∈ H1(ℝN) to the equation −Δu + a(x)u = up, where N ≥ 2, p > 1 with p < 2∗ − 1 = 
and the potential a(x) is a positive function enjoying a planar symmetry. We require suitable decay assumptions which are widely implied by those in [6], in which Wei and Yan have obtained an analogous multiplicity result by using different techniques.
Keywords: Stationary Schrödinger equation in the whole domain; minimax theorem; concentration-compactness methods
Published Online: 2016-03-10
Published in Print: 2012-02-01
© 2016 by Advanced Nonlinear Studies, Inc.
