Multiplicity of k-convex solutions for a singular k-Hessian system

• Autorzy: Yang Zedong , Bai Zhanbing

Identyfikatory

DOI

10.1515/dema-2024-0066

• Języki publikacji: EN

Abstrakty

EN

In this article, we study the following nonlinear k-Hessian system with singular weights [formula], where 𝜆 >0 , 1 ≤𝑘 ≤𝑁 is an integer, Ω stands for the open unit ball in ℝ𝑁 , and 𝑆𝑘(𝜎(𝐷2𝑢)) is the k-Hessian operator of u. By using the fixed point index theory, we prove the existence and nonexistence of negative k-convex radial solutions. Furthermore, we establish the multiplicity result of negative k-convex radial solutions based on a priori estimate achieved. More precisely, there exists a constant 𝜆∗ >0 such that the system admits at least two negative k-convex radial solutions for 𝜆 ∈(0,𝜆∗).

Słowa kluczowe

EN

k-Hessian system; k-convex solution; multiplicity; upper and lower solution

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240066
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Yang Zedong

• College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China

autor

Bai Zhanbing

• College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).