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On the p-Laplacian Kirchhoff–Schrödinger equation with potentials vanishing or unbounded at infinity in R3

This paper mainly deals with a class of the p-Laplacian Kirchhoff–Schrödinger equation with potentials vanishing or unbounded at infinity. We prove the existence and concentration behavior of positive solutions for the problem by the variational methods and concentration-compactness principle. The main feature of this paper is that the potential decays to zero at infinity like | x|− α with 0 < α ≤ 2, and the function K( x) is allowed to be unbounded, which is different from some previous papers.