Periodic n dimensional first order coupled systems and periodic schizophrenia phenomena

Minhós, Feliz; Fialho, João; Sousa, Robert de

doi:10.1016/j.jmaa.2020.124482

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…In [35], the authors developed the existence and localization results to study the existence of solutions for the following fully nonlinear coupled ODSs (notations here are changed from the original paper):…”

Section: Introductionmentioning

confidence: 99%

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New results and applications on the existence results for nonlinear coupled systems

et al. 2021

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In this manuscript, we study a certain classical second-order fully nonlinear coupled system with generalized nonlinear coupled boundary conditions satisfying the monotone assumptions. Our new results unify the existence criteria of certain linear and nonlinear boundary value problems (BVPs) that have been previously studied on a case-by-case basis; for example, Dirichlet and Neumann are special cases. The common feature is that the solution of each BVPs lies in a sector defined by well-ordered coupled lower and upper solutions. The tools we use are the coupled lower and upper solutions approach along with some results of fixed point theory. By means of the coupled lower and upper solutions approach, the considered BVPs are logically modified to new problems, known as modified BVPs. The solution of the modified BVPs leads to the solution of the original BVPs. In our case, we only require the Nagumo condition to get a priori bound on the derivatives of the solution function. Further, we extend the results presented in (Franco et al. in Extr. Math. 18(2):153–160, 2003; Franco et al. in Appl. Math. Comput. 153:793–802, 2004; Franco and O’Regan in Arch. Inequal. Appl. 1:423–430, 2003; Asif et al. in Bound. Value Probl. 2015:134, 2015). Finally, as an application, we consider the fully nonlinear coupled mass-spring model.

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Section: Introductionmentioning

confidence: 99%

“…The approach used in [35] is topological in nature and demonstrated in the forms of differential inequalities (upper and lower solutions).…”

Section: Introductionmentioning

confidence: 99%

New results and applications on the existence results for nonlinear coupled systems

et al. 2021

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Periodic second-order systems and coupled forced Van der Pol oscillators

Minhós,

Perestrelo

2024

J. Fixed Point Theory Appl.

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We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation of the Nagumo condition and the Topological Degree Theory. The localization tool is based on a technique of orderless upper and lower solutions, that involves functions with translations. We apply our result to a system of two coupled Van der Pol oscillators with a forcing component.

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First-order periodic coupled systems with orderless lower and upper solutions

Minhós

Perestrelo

2023

MATH

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<abstract><p>We present some existence and localization results for periodic solutions of first-order coupled nonlinear systems of two equations, without requiring periodicity for the nonlinearities. The arguments are based on Schauder's fixed point theorem together with not necessarily well-ordered upper and lower solutions. A real-case scenario shows the applicability of our results to some population dynamics models, describing the interaction between a criminal and a non-criminal population with a law enforcement component.</p></abstract>

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Periodic n dimensional first order coupled systems and periodic schizophrenia phenomena

Cited by 3 publications

References 18 publications

New results and applications on the existence results for nonlinear coupled systems

New results and applications on the existence results for nonlinear coupled systems

Periodic second-order systems and coupled forced Van der Pol oscillators

First-order periodic coupled systems with orderless lower and upper solutions

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