Abstract
In this study, we investigate the existence of at least one solution and the existence of an infinite number of solutions for a discrete fractional boundary value problem. Requiring an algebraic condition on the nonlinear term for small values of the parameter and requiring an additional asymptotical behavior of the potential at zero, we investigate the existence of at least one nontrivial solution for the problem. Moreover, under suitable assumptions on the oscillatory behavior of the nonlinearity at infinity, for exact collections of the parameter, we discuss the existence of a sequence of solutions for the problem. We also present some examples that illustrate the applicability of the main results.
Recommended Citation
D. Barilla et al., "Existence Results for a Discrete Fractional Boundary Value Problem," Electronic Research Archive, vol. 33, no. 3, pp. 1541 - 1565, AIMS Press, Jan 2025.
The definitive version is available at https://doi.org/10.3934/ERA.2025073
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
discrete fractional; existence of an infinite number of solutions; existence of one solution; variational methods
International Standard Serial Number (ISSN)
2688-1594
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2025 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Jan 2025
