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Search Results (3)

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Keywords = Ambrosetti–Prodi problems

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13 pages, 769 KiB  
Article
On an Ambrosetti-Prodi Type Problem with Applications in Modeling Real Phenomena
by Irina Meghea
Mathematics 2025, 13(14), 2308; https://doi.org/10.3390/math13142308 - 19 Jul 2025
Viewed by 66
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 2nd Edition)
19 pages, 444 KiB  
Article
Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations
by Feliz Minhós and Gracino Rodrigues
Mathematics 2023, 11(17), 3645; https://doi.org/10.3390/math11173645 - 23 Aug 2023
Cited by 2 | Viewed by 1089
Abstract
This paper deals with two types of systems of second-order differential equations with parameters: coupled systems with the boundary conditions of the Sturm–Liouville type and classical systems with Dirichlet boundary conditions. We discuss an Ambosetti–Prodi alternative for each system. For the first type [...] Read more.
This paper deals with two types of systems of second-order differential equations with parameters: coupled systems with the boundary conditions of the Sturm–Liouville type and classical systems with Dirichlet boundary conditions. We discuss an Ambosetti–Prodi alternative for each system. For the first type of system, we present sufficient conditions for the existence and non-existence of its solutions, and for the second type of system, we present sufficient conditions for the existence and non-existence of a multiplicity of its solutions. Our arguments apply the lower and upper solutions method together with the properties of the Leary–Schauder topological degree theory. To the best of our knowledge, the present study is the first time that the Ambrosetti–Prodi alternative has been obtained for such systems with different parameters. Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2023)
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14 pages, 330 KiB  
Article
Bifurcation Results for Periodic Third-Order Ambrosetti-Prodi-Type Problems
by Feliz Minhós and Nuno Oliveira
Axioms 2022, 11(8), 387; https://doi.org/10.3390/axioms11080387 - 7 Aug 2022
Cited by 2 | Viewed by 1756
Abstract
This paper presents sufficient conditions for the existence of a bifurcation point for nonlinear periodic third-order fully differential equations. In short, the main discussion on the parameter s about the existence, non-existence, or the multiplicity of solutions, states that there are some critical [...] Read more.
This paper presents sufficient conditions for the existence of a bifurcation point for nonlinear periodic third-order fully differential equations. In short, the main discussion on the parameter s about the existence, non-existence, or the multiplicity of solutions, states that there are some critical numbers σ0 and σ1 such that the problem has no solution, at least one or at least two solutions if s<σ0, s=σ0 or σ0>s>σ1, respectively, or with reversed inequalities. The main tool is the different speed of variation between the variables, together with a new type of (strict) lower and upper solutions, not necessarily ordered. The arguments are based in the Leray–Schauder’s topological degree theory. An example suggests a technique to estimate for the critical values σ0 and σ1 of the parameter. Full article
(This article belongs to the Collection Differential Equations and Dynamical Systems)
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