Infinitely many positive solutions for the nonlinear Shcrodinger equations in Rⁿ

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We consider the following nonlinear problem in ⁿ eq - Δu +V(|y|)u=uᵖ, u>0 in ⁿ, u ∈ H¹(ⁿ) where V(r) is a positive function, 1<p <N+2/N-2. We show that if V(r) has the following expansion: There are constants a>0, m>1, θ>0, and V₀>0, such that V(r)= V₀+ a rᵐ +O(1rᵐ⁺θ), as r→ +∞, then eq has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.