Infinitely many positive solutions of nonlinear Schrödinger equations

The paper deals with the equation - Δ u+ a(x) u= | u| p-1u, u∈ H1(RN) , with N≥ 2 , p>1,p 0 , lim |x|→∞a(x) = a∞. Assuming that the potential a(x) satisfies lim|x|→∞[a(x)-a∞]eη|x|=∞∀η>0, limρ→∞sup{a(ρθ1)-a(ρθ2):θ1,θ2∈RN,|θ1|=|θ2|=1}eη~ρ=0forsomeη~>0 and other technical conditions, but not requiring any symmetry, the existence of infinitely many positive multi-bump solutions is proved. This result considerably improves those of previous papers because we do not require that a(x) has radial symmetry, or that N= 2 , or that | a(x) - a∞| is uniformly small in RN, etc..