Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian

Advances in Difference Equations

Jufang Wang¹  Boya Zhang¹  Si Wang¹  Changlong Yu² 

[1] College of Sciences, Hebei University of Science and Technology, 050018, Shijiazhuang, Hebei, P.R. China;Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, 100124, Beijing, China;College of Sciences, Hebei University of Science and Technology, 050018, Shijiazhuang, Hebei, P.R. China;

关键词: q;    Positive solutions;    Boundary value problem;    Guo–Krasnoselskii fixed point theorem;   

DOI  :  10.1186/s13662-021-03652-x

来源: Springer

【 摘 要 】

The 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.

【 授权许可】

CC BY