On a class of nonlinear Schrödinger equations in ℝ2 involving critical growth

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Abstract

In this paper we deal with semilinear elliptic problem of the form-ε2Δu+V(z)u=f(u),inℝ2u∈C2(ℝ2)∩H1(Rℝ2), u>0,inℝ2,where ε is a small positive parameter, V:R2→ℝ is a positive potential bounded away from zero, and f(u) behaves like exp(αs2) when s→+∞. We prove the existence of solutions concentrating around a local minima not necessarily nondegenerate of V(x), when ε tends to 0. © 2001 Academic Press.

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Do Ó, M. J., & Souto, M. A. S. (2001). On a class of nonlinear Schrödinger equations in ℝ2 involving critical growth. Journal of Differential Equations, 174(2), 289–311. https://doi.org/10.1006/jdeq.2000.3946

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