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Positive solutions for a nonlocal problem with a convection term and small perturbations
Author(s) -
Liu Jiayin,
Wang Li,
Zhao Peihao
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4003
Subject(s) - mathematics , bounded function , term (time) , boundary value problem , domain (mathematical analysis) , class (philosophy) , mathematical analysis , mountain pass theorem , initial value problem , nonlinear system , physics , quantum mechanics , artificial intelligence , computer science
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.