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Research Article | Open Access

Three nonnegative solutions for Sturm-Liouville BVP and application to the complete Sturm-Liouville equations

Zhongqian Wang, Xuejun Zhang, Mingliang Song( )
School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 210013, China
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Abstract

The main purpose of this manuscript is to investigate the Sturm-Liouville BVP for non-autonomous Lagrangian systems. Under the suitable assumptions, we establish an existence theorem for three nonnegative solutions via Bonanno-Candito's three critical point theory. As an application in the complete Sturm-Liouville equations with Sturm-Liouville BVC, we get an existence theorem of three nonnegative solutions. Meanwhile, we give three examples to show the correctness of our results.

Keywords

Sturm-Liouville BVCLagrangian systemscritical pointsindex theorycomplete Sturm-Liouville equations
CLC number: 34B15, 34B24, 35B38, 58E05, 70H05

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 6543-6558
DOI: 10.3934/math.2023330

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Cite this article:
Wang Z, Zhang X, Song M. Three nonnegative solutions for Sturm-Liouville BVP and application to the complete Sturm-Liouville equations. AIMS Mathematics, 2023, 8(3): 6543-6558. https://doi.org/10.3934/math.2023330

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Received: 18 September 2022
Revised: 24 December 2022
Accepted: 26 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)