Polyharmonic systems involving critical nonlinearities with sign-changing weight functions
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Date
2020-12-10
Authors
Rani, Anu
Goyal, Sarika
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the existence of multiple solutions of the polyharmonic system involving critical nonlinearities with sign-changing weight functions
(-Δ)mu = λƒ(x)|u|r-2u + β/β+γ h(x)|u|β-2 u|v|γ in Ω,
(-Δ)mv = μg(x)|v|r-2v + γ/β+γ h(x)|u|β|v|γ-2v in Ω,
Dku = Dkv = 0 for all |k| ≤ m - 1 on ∂Ω,
where (-Δ)m denotes the polyharmonic operators, Ω is a bounded domain in ℝN with smooth boundary ∂Ω, m ∈ ℕ, N ≥ 2m + 1, 1 < r < 2 and β > 1, γ > 1 satisfying 2 < β + γ ≤ 2*m with 2*m = 2N/N-2m as a critical Sobolev exponent and λ, μ > 0. The functions ƒ, g and h : Ω → ℝ are sign-changing weight functions satisfying ƒ, g ∈ Lα(Ω) respectively. Using the variational methods and Nehari manifold, we prove that the system admits at least two nontrivial solutions with respect to parameter (λ, μ) ∈ ℝ2+ \ {(0, 0)}.
Description
Keywords
Polyharmonic operator system, Sign-changing weight functions, Critical exponent, Nehari manifold, Concave-convex nonlinearities
Citation
Rani, A., & Goyal, S. (2020). Polyharmonic systems involving critical nonlinearities with sign-changing weight functions. <i>Electronic Journal of Differential Equations, 2020</i>(118), pp. 1-25.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.