A Sub-Supersolution Method for p -Laplacian Equation with Non-Local Term

Abstract

This paper is concerned with the existence of solutions for $p$ -Laplace problems with non-local term. We prove the sub-supersolution theorem using the pseudomonotone operator theorem and Minty–Browder theorem with appropriate assumptions on $M,g_i\left(i=\mathrm{1,2}\right)$ . Then, using the sub-supersolution approach, we determine the existence of positive solutions to specific problems.