Properties of Positive Solutions to Sturm-Liouville Boundary Value Problems With <em>p</em>-Laplace Operators

YANG Jing-bao

doi:10.21656/1000-0887.370047

Volume 37 Issue 8

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YANG Jing-bao. Properties of Positive Solutions to Sturm-Liouville Boundary Value Problems With p-Laplace Operators[J]. Applied Mathematics and Mechanics, 2016, 37(8): 856-862. doi: 10.21656/1000-0887.370047

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Properties of Positive Solutions to Sturm-Liouville Boundary Value Problems With p-Laplace Operators

doi: 10.21656/1000-0887.370047

YANG Jing-bao

Department of Education, Bozhou University, Bozhou, Anhui 236800, P.R.China

Received Date: 2016-02-13
Rev Recd Date: 2016-04-20
Publish Date: 2016-08-15

Abstract

Abstract

The properties of positive solutions were investigated for a class of SturmLiouville boundary value problems with p-Laplace operators. Based on the properties of p-Laplace operators, and according to the L’H?pital’s rule and the extreme value theorem for continuous functions on closed intervals, the SturmLiouville boundary value problems with p-Laplace operators were studied. The 2 necessary conditions for the existence of positive solutions were obtained. In the last part, the application of the main findings was given. The work enriches the content in the field of boundary value problems, and provides a new channel of using computer and iterative techniques to find approximate solutions to boundary value problems, meanwhile extending some conclusions in previous literatures.
- p-Laplace operator,
- Sturm-Liouville boundary value problem,
- extreme value theorem

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References

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