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Research Article | Open Access

On a complete parametric Sturm-Liouville problem with sign changing coefficients

Eleonora Amoroso, Giuseppina D'Aguì( ), Valeria Morabito
Department of Engineering, University of Messina, 98166 Messina, Italy
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Abstract

In this paper we study a complete second order differential equation of Sturm-Liouville type under Dirichlet boundary condition and where the variable coefficients are allowed to be sign changing. Through critical point theory, we obtain the existence of two nontrivial generalized solutions by requiring a specific growth on the nonlinearity. Moreover, the solutions turn out to be nonnegative and with opposite energy sign.

Keywords

critical point theorySturm-Liouville equationsnonlinear differential problemsordinary differential equationsmultiple results
CLC number: 34B10

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 6499-6512
DOI: 10.3934/math.2024316

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Cite this article:
Amoroso E, D'Aguì G, Morabito V. On a complete parametric Sturm-Liouville problem with sign changing coefficients. AIMS Mathematics, 2024, 9(3): 6499-6512. https://doi.org/10.3934/math.2024316

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Received: 02 January 2024
Revised: 01 February 2024
Accepted: 04 February 2024
Published: 15 March 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)