Results on the Existence and Multiple Solutions of a p-Kirchhoff Equation with a Subcritical Hardy-Sobolev Exponent and Concave-Convex Nonlinearities

This paper explores the existence and multiplicity of solutions for a specific class of nonlinear boundary value problems with p-Kirchhoff type. The investigation was motivated by C.Caisheng’s idea [1] and the properties of Hardy terms using the Caffarelli-Kohn-Nirenberg Inequality. To achieve these results, we utilized variational methods, specifically the Mountain Pass Theorem and Fountain Theorem, and relied on parameters such as p, q, s, t, \(\lambda \) $\lambda$ , and \(\mu \) $\mu$ to establish a strong foundation.