Our aim in this paper is to study the existence of renormalized solution for a class of nonlinear p(x)-Laplace problems with Neumann nonhomogeneous boundary conditions and diuse Radon measure data which does not charge the sets of zero p(.)-capacity
Abstract. This article is concerned with the existence result of the unilateral problem associated to the equations of the typewhere A is a Leray-Lions operator having a growth not necessarily of polynomial type and φ ∈ C 0 (R, R N ).
In this paper, we construct an integer-valued degree function in a suitable classes of mappings of monotone type, using a complementary system formed of Generalized Sobolev Spaces in which the variable exponent p ∈ P log (Ω) satisfy 1 < p − ≤ p + ≤ ∞, where Ω ⊂ R N is open and bounded. This kind of spaces are not reflexives.
We prove the existence of a weak solution for the nonlinear parabolic initial boundary value problem associated to the equation u t − div a(x, t, u, ∇u) = f (x, t), by using the Topological degree theory for operators of the form L + S, where L is a linear densely dened maximal monotone map and S is a bounded demicontinuous map of class (S + ) with respect to the domain of L. We will therefore use the Topological degree theory to study a parabolic equation in the space L p (0, T ; W 1,p 0 (Ω)) where the exponent p is not necessarily equal to 2 (p ≥ 2).
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