Positive Solutions to the Discrete Boundary Value Problem of the Kirchhoff Type

Bahua Lin and Zhan Zhou ()
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Bahua Lin: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Zhan Zhou: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Mathematics, 2023, vol. 11, issue 16, 1-14

Abstract: The paper aims to study a discrete boundary value problem of the Kirchhoff type based on the critical point theory and the strong maximum principle. Compared to the existing literature, the existence and multiplicity of positive solutions to the problem are considered according to the behavior of the nonlinear term f in some points between the zero and positive infinity, which is a new attempt. Under different assumptions of the nonlinear term f , we obtain the determined open intervals of the parameter λ , such that the problem has at least three positive solutions or at least two positive solutions in different intervals. In the end, two concrete examples are used to illustrate our main conclusions.

Keywords: discrete boundary value problem; positive solutions; critical point theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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