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Research Article | Open Access

Existence and multiplicity of positive solutions for one-dimensional p-Laplacian problem with sign-changing weight

Liangying Miao1, Man Xu2, Zhiqian He3( )
College of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
School of Mathematics and Physics, Qinghai University, Xining 810016, China
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Abstract

In this paper, we show the positive solutions set for one-dimensional p-Laplacian problem with sign-changing weight contains a reversed S-shaped continuum. By figuring the shape of unbounded continuum of positive solutions, we identify the interval of bifurcation parameter in which the p-Laplacian problem has one or two or three positive solutions according to the asymptotic behavior of nonlinear term at 0 and ∞. The proof of the main result is based upon bifurcation technique.

Keywords

p-Laplacian problempositive solutionmultiplicitybifurcationsign-changing weight

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Electronic Research Archive
Volume 31 Issue 6,
June 2023
Pages 3086-3096
DOI: 10.3934/era.2023156

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Cite this article:
Miao L, Xu M, He Z. Existence and multiplicity of positive solutions for one-dimensional p-Laplacian problem with sign-changing weight. Electronic Research Archive, 2023, 31(6): 3086-3096. https://doi.org/10.3934/era.2023156

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Received: 15 January 2023
Revised: 15 February 2023
Accepted: 15 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

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