Variable Exponent Kirchhoff‐Type Problems Involving Singular and Nonlocal Terms on Riemannian Manifolds

ABSTRACT In this paper, we investigate a binonlocal elliptic problem of the ‐Kirchhoff type, incorporating a singular term, within the framework of complete noncompact Riemannian manifolds. Our primary goal is to establish the existence of at least two nontrivial weak solutions, provided that a certain parameter remains sufficiently small. To achieve this, we employ the Nehari manifold method combined with the concept of fibering maps. Specifically, we define the associated Nehari manifold by considering the first derivative of the fibering mapping. Subsequently, we partition the Nehari manifold into three disjoint subsets based on the second derivative of the fibering function. It is shown that the global minimizers of the energy functional, when restricted to two of these subsets, correspond to the desired solutions, while the third subset is empty.