Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients
Article first published online: 14 JUN 2012
Copyright © 2012 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 66, Issue 3, pages 372–413, March 2013
How to Cite
Cerami, G., Passaseo, D. and Solimini, S. (2013), Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients. Comm. Pure Appl. Math., 66: 372–413. doi: 10.1002/cpa.21410
- Issue published online: 21 DEC 2012
- Article first published online: 14 JUN 2012
- Manuscript Revised: AUG 2011
- Manuscript Received: MAR 2011
In this paper the equation is considered, when N ≥ 2, p > 1, and if N ≥ 3. Assuming that the potential a(x) is a positive function belonging to such that a(x) a∞ > 0 as |x|∞ and satisfies slow decay assumptions but does not need to fulfill any symmetry property, the existence of infinitely many positive solutions, by purely variational methods, is proved. The shape of the solutions is described as is, and furthermore, their asymptotic behavior when . © 2012 Wiley Periodicals, Inc.