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Mathematics
Volume 13
Issue 14
10.3390/math13142308
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Article

On an Ambrosetti-Prodi Type Problem with Applications in Modeling Real Phenomena

by
Irina Meghea
1,2
1
Department of Mathematical Methods and Models, Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania
2
Research Center for Environmental Protection and Eco-Friendly Technologies, 1 Polizu Str., 011061 Bucharest, Romania
Mathematics 2025, 13(14), 2308; https://doi.org/10.3390/math13142308 (registering DOI)
Submission received: 30 June 2025 / Revised: 16 July 2025 / Accepted: 17 July 2025 / Published: 19 July 2025
(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 2nd Edition)
Versions Notes

Abstract

This work presents a solving method for problems of Ambrosetti-Prodi type involvingp-Laplacian and p-pseudo-Laplacian operators by using adequate variational methods. A variant of the mountain pass theorem, together with a kind of Palais-Smale condition, is involved in order to obtain and characterize solutions for some mathematical physics issues. Applications of these results for solving some physical chemical problems evolved from the need to model real phenomena are displayed. Solutions for Dirichlet problems containing these two operators applied for modeling critical micellar concentration, as well as the volume fraction of liquid mixtures, have been drawn.
Keywords: Ambrosetti-Prodi type problem; modeling real phenomena; mathematical physics problems; p-Laplacian; p-pseudo-Laplacian; variational methods; Dirichlet problem; Sobolev spaces; critical micellar concentration; volume fraction Ambrosetti-Prodi type problem; modeling real phenomena; mathematical physics problems; p-Laplacian; p-pseudo-Laplacian; variational methods; Dirichlet problem; Sobolev spaces; critical micellar concentration; volume fraction

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MDPI and ACS Style

Meghea, I. On an Ambrosetti-Prodi Type Problem with Applications in Modeling Real Phenomena. Mathematics 2025, 13, 2308. https://doi.org/10.3390/math13142308

AMA Style

Meghea I. On an Ambrosetti-Prodi Type Problem with Applications in Modeling Real Phenomena. Mathematics. 2025; 13(14):2308. https://doi.org/10.3390/math13142308

Chicago/Turabian Style

Meghea, Irina. 2025. "On an Ambrosetti-Prodi Type Problem with Applications in Modeling Real Phenomena" Mathematics 13, no. 14: 2308. https://doi.org/10.3390/math13142308

APA Style

Meghea, I. (2025). On an Ambrosetti-Prodi Type Problem with Applications in Modeling Real Phenomena. Mathematics, 13(14), 2308. https://doi.org/10.3390/math13142308

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