Abstract
AbstractThe aim of this paper is to investigate the boundary value problem of a fractional q-difference equation with ϕ-Laplacian, where ϕ-Laplacian is a generalized p-Laplacian operator. We obtain the existence and nonexistence of positive solutions in terms of different eigenvalue intervals for this problem by means of the Green function and Guo–Krasnoselskii fixed point theorem on cones. Finally, we give some examples to illustrate the use of our results.
Funder
national natural science foundation of china
Natural Science Foundation of Hebei Province
Department of Education of Hebei Province
beijing natural science foundation
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference24 articles.
1. Kac, V., Cheung, P.: Quantum Calculus. Springer, New York (2002)
2. Al-Salam, W.A.: Some fractional q-integrals and q-derivatives. Proc. Edinb. Math. Soc. 15(2), 135–140 (1966)
3. Agarwal, R.P.: Certain fractional q-integrals and q-derivatives. Math. Proc. Camb. Philos. Soc. 66, 365–370 (1969)
4. Han, Z., Lu, H., Zhang, C.: Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian. Appl. Math. Comput. 257, 526–536 (2015)
5. Xu, X., Zhang, H.: Multiple positive solutions to singular positone and semipositone m-point boundary value problems of nonlinear fractional differential equations. Bound. Value Probl. 34, 1–18 (2018)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献