SOLVABILITY FOR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEMS OF BAGLEY-TORVIK EQUATIONS AT RESONANCE

Nan Yao; Xiping Liu; Mei Jia

doi:10.11948/20190289

2020 Volume 10 Issue 5

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Nan Yao, Xiping Liu, Mei Jia. SOLVABILITY FOR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEMS OF BAGLEY-TORVIK EQUATIONS AT RESONANCE[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1937-1953. doi: 10.11948/20190289

Citation:

Nan Yao, Xiping Liu, Mei Jia. SOLVABILITY FOR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEMS OF BAGLEY-TORVIK EQUATIONS AT RESONANCE[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1937-1953. doi: 10.11948/20190289

SOLVABILITY FOR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEMS OF BAGLEY-TORVIK EQUATIONS AT RESONANCE

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Corresponding author: Email address: xipingliu@usst.edu.cn(X. Liu)

Abstract

Abstract

In this paper, we study the solvability for Riemann-Stieltjes integral boundary value problems of Bagley-Torvik equations with fractional derivative under resonant conditions. Firstly, the kernel function is presented through the Laplace transform and the properties of the kernel function are obtained. And then, some new results on the solvability for the boundary value problem are established by using Mawhin's coincidence degree theory. Finally, two examples are presented to illustrate the applicability of our main results.
- Bagley-Torvik equation /
- Caputo derivative /
- Riemann-Stieltjes integral /
- boundary value problem /
- resonant condition /
- Mawhin's coincidence degree theory
MSC: 34A08, 34B10, 26A33

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References

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