Existence of positive solutions for prescribed mean curvature problems with nonlocal term via sub‐ and supersolution method

In this paper, we are concerned with the existence of solution to the class of nonlocal quasilinear problem of the type− div ( a ( | ∇ u |2 ) ∇ u ) = f ( x , u , B ( u ) ) in Ω ,u = 0 on ∂ Ω ,( P )where Ω is a smooth bounded domain onℝ N , a : ℝ + → ℝ + , f : Ω × ℝ × ℝ → ℝ , and B : L ∞ ( Ω ) → ℝ are functions whose hypotheses will be detailed later. We use sub‐ and supersolution method to find solutions to problem ( P ). Further, we apply our result to some specific nonlocal prescribed mean curvature problems.