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. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 12:1(2012), pp. 173-186. [10.1515/ans-2012-0110]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
