Polyharmonic systems involving critical nonlinearities with sign-changing weight functions
| dc.contributor.author | Rani, Anu | |
| dc.contributor.author | Goyal, Sarika | |
| dc.date.accessioned | 2021-10-11T19:31:17Z | |
| dc.date.available | 2021-10-11T19:31:17Z | |
| dc.date.issued | 2020-12-10 | |
| dc.description.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)}. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 25 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Rani, A., & Goyal, S. (2020). Polyharmonic systems involving critical nonlinearities with sign-changing weight functions. Electronic Journal of Differential Equations, 2020(118), pp. 1-25. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14630 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Polyharmonic operator system | |
| dc.subject | Sign-changing weight functions | |
| dc.subject | Critical exponent | |
| dc.subject | Nehari manifold | |
| dc.subject | Concave-convex nonlinearities | |
| dc.title | Polyharmonic systems involving critical nonlinearities with sign-changing weight functions | |
| dc.type | Article |