Existence of multiple solutions of p-fractional Laplace operator with sign-changing weight function
نویسندگان
چکیده
منابع مشابه
Existence 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 کاملEXISTENCE OF POSITIVE AND SIGN-CHANGING SOLUTIONS FOR p-LAPLACE EQUATIONS WITH POTENTIALS IN R
We study the perturbed equation −ε div(|∇u|p−2∇u) + V (x)|u|p−2u = h(x, u) + K(x)|u| −2u, x ∈ R u(x)→ 0 as |x| → ∞ . where 2 ≤ p < N , p∗ = pN N−p , p < q < p ∗. Under proper conditions on V (x) and h(x, u), we obtain the existence and multiplicity of solutions. We also study the existence of solutions which change sign.
متن کاملExistence 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...
متن کاملMULTIPLE SOLUTIONS FOR THE p−LAPLACE OPERATOR WITH CRITICAL GROWTH
In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation −∆pu = |u| ∗ u + λf(x, u) in a smooth bounded domain Ω of R with homogeneous Dirichlet boundary conditions on ∂Ω, where p = Np/(N − p) is the critical Sobolev exponent and ∆pu = div(|∇u|∇u) is the p−laplacian. The proof is based on variational arguments and the classical con...
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 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: Advances in Nonlinear Analysis
سال: 2015
ISSN: 2191-950X,2191-9496
DOI: 10.1515/anona-2014-0017