Existence of three solutions for two quasilinear Laplacian systems on graphs

• Autorzy: Pang Yan , Zhang Xingyong

Identyfikatory

DOI

10.1515/dema-2024-0062

• Języki publikacji: EN

Abstrakty

EN

We deal with the existence of three distinct solutions for a poly-Laplacian system with a parameter on finite graphs and a (p,q) -Laplacian system with a parameter on locally finite graphs. The main tool is an abstract critical point theorem in [G. Bonanno and S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal. 89 (2010), no. 1, 1–10]. A key point in this study is that we overcome the difficulty to prove that the Gâteaux derivative of the variational functional for poly-Laplacian operator admits a continuous inverse, which is caused by the special definition of the poly-Laplacian operator on graph and mutual coupling of two variables in system.

Słowa kluczowe

EN

critical point theorem; ploy-Laplacian system; finite graph; locally finite graph; nontrivial solution

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240062
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Pang Yan

• Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan, 650500, P. R. China

autor

Zhang Xingyong

• Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan, 650500, P. R. China
• Research Center for Mathematics and Interdisciplinary Sciences, Kunming University of Science and Technology, Kunming, Yunnan, 650500, P. R. China

Bibliografia

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• [11] G. Bonanno and S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal. 89 (2010), no. 1, 1–10, DOI: https://doi.org/10.1080/00036810903397438.
• [12] G. Bonanno and G. M Bisci, Three weak solutions for elliptic Dirichlet problems, J. Math. Anal. Appl. 382 (2011), no. 1, 1–8, DOI: https://doi.org/10.1016/j.jmaa.2011.04.026.
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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).