Abstract
In this article, we study the existence and multiplicity of solutions for a class of anisotropic elliptic equations First we establisch that anisotropic space is separable and by using the Fountain theorem, and dual Fountain theorem we prove, under suitable conditions, that the problem (P) admits two sequences of weak solutions.
Highlights
Let Ω ⊂ RN (N ≥ 3) be a bounded domain with smooth boundary
First we establisch that anisotropic space is separable and by using the Fountain theorem, and dual Fountain theorem we prove, under suitable conditions, that the problem (P ) admits two sequences of weak solutions
In this paper we will study the multiplicity of weak solutions of the anisotropic problem: ( (P )
Summary
Let Ω ⊂ RN (N ≥ 3) be a bounded domain with smooth boundary. In this paper we will study the multiplicity of weak solutions of the anisotropic problem:. Ω, u = 0 on ∂Ω, and they considered f (x, u) = λ|u|q(x)−2u + μ|u|γ(x)−2u, where λ and μ are constant, and they established the existence of two unbounded sequences of weak solutions, their proof is based on Fountain theorem [20] This kind of equation are treated in several works by many authors , we refer here to the articles ( [3], [6], [15], [16]). If −→p : Ω → RN ; −→p (x) = (p1(x), p2(x), ..., pN (x)), and for each i ∈ {1, 2, ..., N }, we have pi ∈ C+(Ω), and satisfy (1.1), the anisotropic variable exponent Sobolev space W01,−→p (x)(Ω) is defined as the closure of C0∞(Ω) under the norm. In the first section we will give some known results, in the second we will give the proof of our main results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
