Super‐Subsolution Methods for Nonlocal Problems With Semipositone Nonlinearities

Abstract

ABSTRACT In this paper, we investigate a class of nonlocal Kirchhoff‐type problems in Orlicz–Sobolev spaces, involving strongly perturbed singular terms and Heaviside‐type discontinuous nonlinearities. By combining the monotone operator theory with the method of super‐ and subsolutions, we establish the existence and multiplicity of positive solutions. Our results extend previous works on ‐Laplacian and nonlocal Kirchhoff problems by addressing more general nonlinearities, including semipositone and concave‐convex cases. Several illustrative examples are provided to demonstrate the applicability of our approach.