Solvability for some fourth order two-point boundary value problems

Zhanbing Bai; Wen Lian; Yongfang Wei; Sujing Sun; Zhanbing Bai; Wen Lian; Yongfang Wei; Sujing Sun

doi:10.3934/math.2020319

AIMS Mathematics

2020, Volume 5, Issue 5: 4983-4994. doi: 10.3934/math.2020319

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Solvability for some fourth order two-point boundary value problems

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China

Received: 22 April 2020 Accepted: 04 June 2020 Published: 09 June 2020
MSC : 34A08, 34B15, 35J05

Some fourth-order two-point boundary value problems are considered in this paper. Firstly, the Green's function is obtained by the use of the Laplace transform. Secondly, the first eigenvalue is given by using Ritz method. Then, by the use of the properties of self-adjoint operators and the fixed point index theory, the existence of positive solutions is obtained. Finally, an example is given to illustrate the main results.
- Laplace transform,
- eigenvalue,
- self-adjoint operators,
- fixed point index
Citation: Zhanbing Bai, Wen Lian, Yongfang Wei, Sujing Sun. Solvability for some fourth order two-point boundary value problems[J]. AIMS Mathematics, 2020, 5(5): 4983-4994. doi: 10.3934/math.2020319

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Abstract

Some fourth-order two-point boundary value problems are considered in this paper. Firstly, the Green's function is obtained by the use of the Laplace transform. Secondly, the first eigenvalue is given by using Ritz method. Then, by the use of the properties of self-adjoint operators and the fixed point index theory, the existence of positive solutions is obtained. Finally, an example is given to illustrate the main results.

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