Infinitely Many Solutions for Partial Discrete Kirchhoff Type Problems Involving p-Laplacian
Abstract
:1. Introduction
- (1)
- This paper is the first time to consider the infinitely many solutions of the partial discrete Kirchhoff-type problems involving p-Laplacian, which are more complex to deal with.
- (2)
- The difficulty to be overcome in this paper is the estimation of in Theorem 1.
- (3)
- To prove the existence of infinitely many solutions of the partial discrete Kirchhoff-type problems involving p-Laplacian, we use critical point theory. Further, by virtue of the strong maximum principle we have established, we acquire some sufficient conditions for the presence of infinitely many positive solutions to the boundary value problems.
- (4)
- We give one example to illustrate our conclusion.
2. Preliminaries
- If , then, for each , the following alternative holds: either
- possesses a global minimum, or
- there is a sequence of critical points (local minima) of such that .
3. Main Results
4. An Example
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Xiong, F. Infinitely Many Solutions for Partial Discrete Kirchhoff Type Problems Involving p-Laplacian. Mathematics 2023, 11, 3288. https://doi.org/10.3390/math11153288
Xiong F. Infinitely Many Solutions for Partial Discrete Kirchhoff Type Problems Involving p-Laplacian. Mathematics. 2023; 11(15):3288. https://doi.org/10.3390/math11153288
Chicago/Turabian StyleXiong, Feng. 2023. "Infinitely Many Solutions for Partial Discrete Kirchhoff Type Problems Involving p-Laplacian" Mathematics 11, no. 15: 3288. https://doi.org/10.3390/math11153288
APA StyleXiong, F. (2023). Infinitely Many Solutions for Partial Discrete Kirchhoff Type Problems Involving p-Laplacian. Mathematics, 11(15), 3288. https://doi.org/10.3390/math11153288