Nontrivial weak solutions for nonlocal nonhomogeneous elliptic problems. Issue 4 (4th March 2022)

• Record Type: Journal Article
• Authors: Zaouche, Elmehdi
• Is Part Of: Applicable analysis. Volume 101:Issue 4(2022)
• Page Start: 1261
• Page End: 1270
• Publication Date: 2022-03-04
• Subjects: M. Mei; Schauder and Tychonoff fixed-point theorems -- nonlocal nonhomogeneous elliptic problem -- homogeneous Dirichlet boundary condition -- weak solution -- existence; 35A05 -- 35J60 -- 35J25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1778674
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This article concerns the following class of nonlocal nonhomogeneous elliptic problems: 1 − ∫ Ω g ( x, u ) d x β div ⁡ ( a ( x ) ∇ u ) = ( g ( x, u ) ) α i n Ω, u = 0 o n ∂ Ω, where Ω is a bounded domain of R n ( n ≥ 1 ), α, β ∈ R, a ( x ) is a matrix with variable coefficients and g : Ω × R → R is a positive function which are defined almost everywhere with respect to the variable x . By using the Schauder and Tychonoff fixed-point theorems, we establish two existence theorems of weak solutions for this problem according to two bundles of hypotheses on α, β and g .