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Research Article | Open Access

ϕ −Laplacian second-order boundary value problems with parameters

Feliz Minhós1,2( ), Nuno Oliveira2
Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora, Portugal
Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
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Abstract

This paper deals with a second-order fully differential equation involving a ϕ −Laplacian operator, which generalizes the more common p-Laplacian, with a parameter, applied to a nonlinearity depending on the unknown function and its first derivative. The main result states the problem's solvability for parameter values for which there are lower and upper solutions for the problem. Singular ϕ −Laplacians considered with an application to the special relativity field.

Keywords

lower and upper solutionsNagumo conditionregular and singular ϕ−Laplacian equationsfixed-point theory

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Electronic Research Archive
Volume 34 Issue 5,
May 2026
Pages 2760-2773
DOI: 10.3934/era.2026126

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Cite this article:
Minhós F, Oliveira N. ϕ −Laplacian second-order boundary value problems with parameters. Electronic Research Archive, 2026, 34(5): 2760-2773. https://doi.org/10.3934/era.2026126

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Received: 08 January 2026
Revised: 15 March 2026
Accepted: 23 March 2026
Published: 15 May 2026
©2026 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)