We show the variational structure of a multiplicity result of positive solutions u is an element of H(1) (R(N)) to the equation -Delta u + a(x)u = u(p), where N >= 2, p > 1 with p < 2* - 1 = N+2/N-2 if N >= 3 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.
Min-Max Solutions to Some Scalar Field Equations
DEVILLANOVA, Giuseppe;SOLIMINI, Sergio Fausto
2012-01-01
Abstract
We show the variational structure of a multiplicity result of positive solutions u is an element of H(1) (R(N)) to the equation -Delta u + a(x)u = u(p), where N >= 2, p > 1 with p < 2* - 1 = N+2/N-2 if N >= 3 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.File in questo prodotto:
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