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On existence solution for Schrödinger–Kirchhoff-type equations involving the fractional p-Laplacian in ℝN

ABSTRACT The aim of this paper is to study the existence solution for Schrödinger–Kirchhoff-type equations involving nonlocal p-fractional Laplacian where is a real positive parameter, is a continuous function, is a singular kernel function, is a nonlocal fractional operator, with f is a Carathéodory function on satisfying the Ambrosetti–Rabinowitz-type condition. Using Mountain Pass Theorem, we obtain the existence of above equations. Our result is a extension the problem studied by Pucci–Xiang–Zhang [1].