existence and multiplicity of nontrivial solutions for $p$-laplacian system with nonlinearities of concave-convex type and sign-changing weight functions
نویسندگان
چکیده
this paper is concerned with the existence of multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions. with the help of the nehari manifold and palais-smale condition, we prove that the system has at least two nontrivial positive solutions, when the pair of parameters $(lambda,mu)$ belongs to a certain subset of $mathbb{r}^2$.
منابع مشابه
Existence and multiplicity of nontrivial solutions for $p$-Laplacian system with nonlinearities of concave-convex type and sign-changing weight functions
This paper is concerned with the existence of multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions. With the help of the Nehari manifold and Palais-Smale condition, we prove that the system has at least two nontrivial positive solutions, when the pair of parameters $(lambda,mu)$ belongs to a c...
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In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.
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and Applied Analysis 3 Theorem 1.3 see 5 . There exists λ0 > 0 such that 1.4 admits exactly two solutions for λ ∈ 0, λ0 , exactly one solution for λ λ0, and no solution for λ > λ0. To proceed, wemake somemotivations of the present paper. Recently, in 6 the author has considered 1.2 with subcritical nonlinearity of concave-convex type, g ≡ 1, and f is a continuous function which changes sign in ...
متن کاملExistence of multiple positive solutions for a p-Laplacian system with sign-changing weight functions
A p-Laplacian system with Dirichlet boundary conditions is investigated. By analysis of the relationship between the Nehari manifold and fibering maps, we will show how the Nehari manifold changes as λ,μ varies and try to establish the existence of multiple positive solutions. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملmultiplicity of positive solutions of laplacian systems with sign-changing weight functions
in this paper, we study the multiplicity of positive solutions for the laplacian systems with sign-changing weight functions. using the decomposition of the nehari manifold, we prove that an elliptic system has at least two positive solutions.
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...
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bulletin of the iranian mathematical societyجلد ۴۰، شماره ۵، صفحات ۱۳۰۱-۱۳۲۶
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