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Research Article | Open Access

Resonance with Landesman-Lazer conditions for parameter-dependent equations: a multiplicity result via the Poincaré-Birkhoff theorem

Chunlian Liu1, Shuang Wang2, Fanfan Chen3( )
School of Mathematics and Statistics, Nantong University, Nantong 226019, China
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224051, China
School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
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Abstract

We investigate the resonance problem and prove the existence of multiple periodic solutions to a second order parameter-dependent equation x″+f(t,x)=sp(t). We weaken the usual requirement on the sublinearity of perturbations when |x| becomes large; and develop a more general method to investigate the rotational characterizations of the Landesman-Lazer conditions. Furthermore, f does not satisfy the common sign condition, and even the global existence of the solution is not guaranteed.

Keywords

periodic solutionsPoincaré-Birkhoff theoremresonanceLandesman-Lazer conditionsparameter-dependent
CLC number: 34B15, 34C15, 34C25

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 28320-28340
DOI: 10.3934/math.20241374

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Cite this article:
Liu C, Wang S, Chen F. Resonance with Landesman-Lazer conditions for parameter-dependent equations: a multiplicity result via the Poincaré-Birkhoff theorem. AIMS Mathematics, 2024, 9(10): 28320-28340. https://doi.org/10.3934/math.20241374

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Received: 08 August 2024
Revised: 21 September 2024
Accepted: 26 September 2024
Published: 15 October 2024
©2024 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)