This paper examines a class of Kirchhoff nonlocal operators involving concave-convex nonlinearities and sign-changing weight functions. With the aid of the Nehari manifold, the existence of multiple nontrivial nonnegative solutions is obtained.
"Multiple solutions for a Kirchhoff-type problem involving nonlocal fractional $p$-Laplacian and concave-convex nonlinearities." Rocky Mountain J. Math. 47 (6) 1803 - 1823, 2017. https://doi.org/10.1216/RMJ-2017-47-6-1803