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Existence of positive solutions for prescribed mean curvature problems with nonlocal term via sub‐ and supersolution method
Author(s) -
Figueiredo Giovany,
Suarez Antonio
Publication year - 2020
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.6505
Subject(s) - mathematics , curvature , bounded function , term (time) , domain (mathematical analysis) , class (philosophy) , type (biology) , mean curvature , mathematical analysis , mathematical optimization , geometry , computer science , artificial intelligence , ecology , physics , quantum mechanics , biology
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.