Abstract
In this paper, we investigate a mixed fractional integral boundary value problem with p(t)-Laplacian operator. Firstly, we derive the Green function through the direct computation and obtain the properties of Green function. For \(p(t)\ne \) constant, under the appropriate conditions of the nonlinear term, we establish the existence result of at least one positive solution of the above problem by means of the Leray–Schauder fixed point theorem. Meanwhile, we also obtain the positive extremal solutions and iterative schemes in view of applying a monotone iterative method. For \(p(t)=\) constant, by using Guo–Krasnoselskii fixed point theorem, we study the existence of positive solutions of the above problem. These results enrich the ones in the existing literatures. Finally, some examples are included to demonstrate our main results in this paper and we give out an open problem.
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Acknowledgements
This research is supported by the National Natural Science Foundation of China (Nos. 11761038, 11761039), the Science and Technology Project of Department of Education of Jiangxi Province (No. GJJ180583).
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Tang, X., Luo, J., Zhou, S. et al. Existence of positive solutions of mixed fractional integral boundary value problem with p(t)-Laplacian operator. Ricerche mat 71, 477–492 (2022). https://doi.org/10.1007/s11587-020-00542-4
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DOI: https://doi.org/10.1007/s11587-020-00542-4
Keywords
- Positive solution
- Mixed fractional integral boundary value problem
- p(t)-Laplacian operator
- Fixed point theorem
- Monotone iterative method