EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC SYSTEMS INVOLVING CRITICAL HARDY–SOBOLEV EXPONENTS AND SIGN-CHANGING WEIGHT FUNCTION
نویسندگان
چکیده
منابع مشابه
ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS
In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...
متن کاملMultiple results for critical quasilinear elliptic systems involving concave-convex nonlinearities and sign-changing weight functions∗
This paper is devoted to study the multiplicity of nontrivial nonnegative or positive solutions to the following systems −4pu = λa1(x)|u|q−2u + b(x)Fu(u, v), in Ω, −4pv = λa2(x)|v|q−2v + b(x)Fv(u, v), in Ω, u = v = 0, on ∂Ω, where Ω ⊂ R is a bounded domain with smooth boundary ∂Ω; 1 < q < p < N , p∗ = Np N−p ; 4pw = div(|∇w|p−2∇w) denotes the p-Laplacian operator; λ > 0 is a positive pa...
متن کاملExistence of Positive Solutions for Quasilinear Elliptic Systems with Sobolev Critical Exponents
In this paper, we consider the existence of positive solutions to the following problem ⎪⎪⎨ ⎪⎪⎩ −div(|∇u|p−2∇u) = ∂F ∂u (u,v)+ ε p−1g(x) in Ω, −div(|∇v|q−2∇v) = ∂F ∂v (u,v)+ εq−1h(x) in Ω, u,v > 0 in Ω, u = v = 0 on ∂Ω, where Ω is a bounded smooth domain in RN ; F ∈C1((R+)2,R+) is positively homogeneous of degree μ ; g,h ∈C1(Ω)\{0} ; and ε is a positive parameter. Using sub-supersolution method...
متن کاملMultiplicity of positive solutions for critical singular elliptic systems with sign - changing weight function ∗
In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.
متن کاملMultiple Positive Solutions for a Quasilinear Elliptic System Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions
Let Ω 0 be an-open bounded domain in R N ≥ 3 and p∗ pN/ N − p . We consider the following quasilinear elliptic system of two equations inW 0 Ω ×W 1,p 0 Ω : −Δpu λf x |u|q−2u α/ α β h x |u|α−2u|v|β,−Δpv μg x |v|q−2v β/ α β h x |u|α|v|β−2v, where λ, μ > 0, Δp denotes the p-Laplacian operator, 1 ≤ q < p < N,α, β > 1 satisfy p < α β ≤ p∗, and f, g, h are continuous functions on Ω which are somewher...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2012
ISSN: 1392-6292,1648-3510
DOI: 10.3846/13926292.2012.685956