Abstract
We consider the nonlinear Schrodinger equation $$-\Delta{u} + V (x)u = K(x)u^3/(1 + u^2)$$ in \({\mathbb {R}^N}\) , and assume that V and K are invariant under an orthogonal involution. Moreover, V and K converge to positive constants V∞ and K∞, as |x| → ∞. We present some results on the existence of a particular type of sign changing solution, which changes sign exactly once. The basic tool employed here is the Concentration–Compactness Principle and the interaction between translated solutions of the corresponding autonomous problem.
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