Lower and Upper Solutions for Even Order Boundary Value Problems

Cabada, Alberto; López-Somoza, Lucía

doi:10.3390/math7100878

Cited by 7 publications

(7 citation statements)

References 22 publications

(33 reference statements)

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“…The dose-response curves of the analgesic effect of propranolol in female and male rats, stressed or not, were compared using the sigmoid dose-effect model. The model, as follows, is derived from Hill's equation [32]:…”

Section: Discussionmentioning

confidence: 99%

“…The dose–response curves of the analgesic effect of propranolol in female and male rats, stressed or not, were compared using the sigmoid dose–effect model. The model, as follows, is derived from Hill's equation [32]: Y = Y min + ( Y max × Y min )/(1 + 10 ^ (log EC 50 × X )), where X is the log of different doses of propranolol, and Y is the nociceptive behavior induced by co‐administration of propranolol with equi‐nociceptive concentrations of formalin. The EC 50 serves as a numerical representation of a drug's potency and is defined as the concentration at which the drug achieves 50% of its maximum effect [33].…”

Section: Methodsmentioning

confidence: 99%

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Effect of propranolol on temporomandibular joint pain in repeatedly stressed rats

Zanelatto,

Vieira,

Nishijima

et al. 2023

European J Oral Sciences

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Stress substantially increases the risk of developing painful temporomandibular disorders (TMDs) by influencing the release of endogenous catecholamines. Propranolol, an antagonist of β‐adrenergic receptors, has shown potential in alleviating TMD‐associated pain, particularly when the level of catecholamines is elevated. The aim of this study was to explore whether intra‐articular propranolol administration is effective in diminishing temporomandibular joint (TMJ) pain during repeated stress situations. Additionally, we investigated the effect of repeated stress on the expression of genes encoding β‐adrenoceptors in the trigeminal ganglion. In the present study, rats were exposed to a stress protocol induced by sound, then to the administration of formalin in the TMJ (to elicit a nociceptive response), followed immediately afterward by different doses of propranolol, after which the analgesic response to propranolol was evaluated. We also assessed the levels of beta‐1 and beta‐2 adrenergic receptor mRNAs (Adrb1 and Adrb2, respectively) using reverse transcription–quantitative PCR (RT‐qPCR). Our findings revealed that propranolol administration reduces formalin‐induced TMJ nociception more effectively in stressed rats than in non‐stressed rats. Furthermore, repeated stress decreases the expression of the Adrb2 gene within the trigeminal ganglion. The findings of this study are noteworthy as they suggest that individuals with a chronic stress history might find potential benefits from β‐blockers in TMD treatment.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Effect of propranolol on temporomandibular joint pain in repeatedly stressed rats

Zanelatto,

Vieira,

Nishijima

et al. 2023

European J Oral Sciences

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“…15 Some other works related to existence of solutions to multi-point BVPs can be found in other studies. 9,[16][17][18][19][20][21] In previous studies, [22][23][24] authors considered second-order nonlinear m-point Neumann BVPs at resonance. Under some sufficient conditions, they proved the existence of at least one solution by using the coincidence degree theory.…”

Section: Introductionmentioning

confidence: 99%

“…The multi‐point linear second‐order ordinary differential equations (ODEs) were first studied by II'in and Moiseev 15 . Some other works related to existence of solutions to multi‐point BVPs can be found in other studies 9,16–21 . In previous studies, 22–24 authors considered second‐order nonlinear

m

‐point Neumann BVPs at resonance.…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for a class of nonlinear Neumann boundary value problems in the presence of upper and lower solutions

Urus

Verma

2022

Math Methods in App Sciences

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In this article, we explore the monotone iterative technique (MI-technique) to study the existence of solutions for a class of nonlinear Neumann four-point, boundary value problems (BVPs) defined as,Using lower solution l(z) and upper solutions u(z), we develop MI-technique, which is based on quasilinearization. To construct the sequences of upper and lower solutions which are monotone, we prove maximum principle as well as anti-maximum principle. Then under certain assumptions, we prove that these sequences converge uniformly to the solution 𝜙(z) in the specific region, where (𝜕G∕𝜕𝜙) < 0 or (𝜕G∕𝜕𝜙) > 0. To demonstrate that the proposed technique is effective, we compute the solution of the nonlinear multi-point BVPs. We don't require sign restriction on G which is very common and strict condition.

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“…More recently on [5], Cabada and Somoza extensively study a family of problems involving Lidstone boundary conditions type. The existence of solution is proved through the usage of lower and upper solutions.…”

Section: Introductionmentioning

confidence: 99%

On Coupled Systems of Lidstone-Type Boundary Value Problems

Sousa

Minhós

Fialho

2021

Mathematical Modelling and Analysis

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This research concerns the existence and location of solutions for coupled system of differential equations with Lidstone-type boundary conditions. Methodology used utilizes three fundamental aspects: upper and lower solutions method, degree theory and nonlinearities with monotone conditions. In the last section an application to a coupled system composed by two fourth order equations, which models the bending of coupled suspension bridges or simply supported coupled beams, is presented.

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Lower and Upper Solutions for Even Order Boundary Value Problems

Cited by 7 publications

References 22 publications

Effect of propranolol on temporomandibular joint pain in repeatedly stressed rats

Effect of propranolol on temporomandibular joint pain in repeatedly stressed rats

Existence of solutions for a class of nonlinear Neumann boundary value problems in the presence of upper and lower solutions

On Coupled Systems of Lidstone-Type Boundary Value Problems

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