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