Positive solutions for a nonlocal problem with a convection term and small perturbations

This paper is concerned with the existence of positive solutions to a class of nonlocal boundary value problem of the p ‐Kirchhoff type− M x , ∫ Ω | ∇ u | p d xΔ p u = f ( x , u , | ∇ u | p − 2 ∇ u ) + λg ( x , u ) in Ω ,u = 0 on ∂ Ω ,where Ω ⊆ R N ( N ≥ 3 ) is a bounded smooth domain and M , f , and g are continuous functions. The existence of a positive solution is stated through an iterative method based on mountain pass theorem. Copyright © 2016 John Wiley & Sons, Ltd.