Abstract
In this paper, we study the p(x)-biharmonique problem with Neumannboundary conditions. Using the three critical point Theorem, we establish the existence of at least threesolutions of this problem.
Highlights
Abdel Rachid El Amrouss, Fouzia Moradi, Mimoun Moussaoui abstract: In this paper, we study the following problem with Neumann boundary conditions
We proves the existence of at least three weak solutions of the above problem, under the following assumptions (f1) For all (x, s) ∈ Ω × R
This paper is divided into four sections, organized as follows: In section 2, we introduce some basic properties of the Lebesgue and Sobolev spaces with variable exponent
Summary
Multiplicity of Solutions for a p(x)-biharmonic Neumann Problem where p ∈ C+ Ω and. Denote p+ = maxp(x), p− = minp(x), x∈Ω x∈Ω and for all x ∈ Ω and k ≥ 1 p∗ (x) :=. +∞ if kp(x) ≥ N. u (x) λ p(x) dx and the space Lp(x) (Ω) , |.|p(x) is a Banach. The space Lp(x) (Ω) , |.|p(x) is separable, uniformly convex, reflexive and its conjugate space is Lq(x) (Ω) where q(x) is the conjugate function of p(x), i.e. ∂xα1 1 ∂xα2 2 ...∂xαNN (the derivation in distributions sense) with α (α1, ..., αN )
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