Abstract
In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type Au+g(x,u,∇u)=f- div F, where A is a Leray-Lions operator and g is a Carathéodory function having natural growth with respect to |∇u| and satisfying the sign condition. The second term is such that, f∈L 1 (Ω) and F∈Π i=1 N L p ′ (Ω,w i 1-p ′ ).
Highlights
Let Ω be a bounded open set of RN, p be a real number such that 1 < p < ∞and w = {wi (x), 0 ≤ i ≤ N } be a vector of weight functions on Ω, i.e.each wi (x) is a measurable a.e. strictly positive function on Ω, satisfying some integrability conditions
We consider the obstacle problem associated to the following differential equations
As regards the second member, we suppose that f ∈ L1 (Ω) and that
Summary
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