Existence of a positive solution to kirchhoff problems involving the fractional laplacian

Abstract

The goal of this paper is to establish the existence of a positive solution to the following fractional Kirchhoff-type problem (eqution preseted) where N ≥ 2, ≥ ≥ 0 is a parameter, α 2 (0; 1), (-δ)α stands for the fractional Laplacian, f ε C(ℝ+,ℝ+). Using a variational method combined with suitable truncation techniques, we obtain the existence of at least one positive solution without compactness conditions.