In this paper, we study a general class of nonlinear anisotrpic elliptic problems associated with the differential inclusion β(u) - div(a(x, D(u) + F(u)) ∋ f in Ω, where f ∈ L∞(Ω). A vector field a(. , .) is a Caratheodory function. Using trunction techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for L∞-data.

The aim of this work is to study the stability for some linear partial functional differential equations. We assume that the linear part is non-densely defined and satisfies the Hille-Yosida condition. Using the positiveness, we give nessecary and sufficient conditions independently of the delay to ensure the uniform exponential stability of the solution semigroup. An application is given for a reaction diffusion equation with several delays.2000 Mathematics Subject Classification: 34K20, 34K30, 34K40.

No abstract

No abstract

No abstract