Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients



In this paper the equation equation image is considered, when N ≥ 2, p > 1, and equation image if N ≥ 3. Assuming that the potential a(x) is a positive function belonging to equation image 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 equation image. © 2012 Wiley Periodicals, Inc.