Infinitely many positive standing waves for Schrödinger equations with competing coefficients

The article deals with the equation Delta u+ a(x)u + b(x)u(q) - u(p) = 0 u is an element of H-1 (R-N), with N > 2,1 < q 3, infa> 0 a(x) -> a(infinity) and b(x) -> 0 as vertical bar x vertical bar -> infinity When (2(X) < a. and b(x) 0, only a finite number of positive solutions to the problem is reasonably. expected. Here we prove that the, presence of a nonzero term b(x)Liq with b(x) > 0, b(x) 4 0, under suitable assumptions on the decay rates of a and b, allows to obtain infinitely many posiive solutions.