Polyharmonic systems involving critical nonlinearities with sign-changing weight functions

dc.contributor.authorRani, Anu
dc.contributor.authorGoyal, Sarika
dc.date.accessioned2021-10-11T19:31:17Z
dc.date.available2021-10-11T19:31:17Z
dc.date.issued2020-12-10
dc.description.abstractThis 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)}.
dc.description.departmentMathematics
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationRani, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14630
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectPolyharmonic operator system
dc.subjectSign-changing weight functions
dc.subjectCritical exponent
dc.subjectNehari manifold
dc.subjectConcave-convex nonlinearities
dc.titlePolyharmonic systems involving critical nonlinearities with sign-changing weight functions
dc.typeArticle

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