Multiple positive solutions for a Choquard equation involving both concave-convex and Hardy-Littlewood-Sobolev critical exponent
نویسندگان
چکیده
منابع مشابه
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملMultiplicity of Positive Solutions for Weighted Quasilinear Elliptic Equations Involving Critical Hardy-Sobolev Exponents and Concave-Convex Nonlinearities
and Applied Analysis 3 When a 0, we set s dp∗ 0, d and t bp∗ 0, b , then 1.1 is equivalent to the following quasilinear elliptic equations: −div ( |∇u|p−2∇u ) − μ |u| p−2u |x| |u|p t −2u |x| λ |u|q−2u |x| in Ω, u 0 on ∂Ω, 1.7 where λ > 0, 1 < p < N, 0 ≤ μ < μ N − p /p , 0 ≤ s, t < p, 1 ≤ q < p and p∗ t p N − t / N − p . Such kind of problem relative with 1.7 has been extensively studied by many...
متن کاملMultiple Positive Solutions for Equations Involving Critical Sobolev Exponent in R N
This article concerns with the problem ?div(jruj m?2 ru) = hu q + u m ?1 ; in R N : Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of > 0 such that there are at least two non-negative solutions for each in (0;).
متن کاملMultiple positive solutions for a class of quasi-linear elliptic equations involving concave-convex nonlinearities and Hardy terms
where Ω ⊂ R is a smooth domain with smooth boundary ∂Ω such that 0 Î Ω, Δpu = div(|∇u|∇u), 1 < p < N, μ < μ̄ = ( N−p p ), l >0, 1 < q < p, sign-changing weight functions f and g are continuous functions on ̄, μ̄ = ( N−p p ) p is the best Hardy constant and p∗ = Np N−p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the multiplicity of positive solu...
متن کاملOn Multiple Solutions for a Singular Quasilinear Elliptic System Involving Critical Hardy-sobolev Exponents
This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...
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: Differential Equations & Applications
سال: 2017
ISSN: 1847-120X
DOI: 10.7153/dea-2017-09-34