On a generalization of the Miranda Theorem and its application to boundary value problems

Szymańska‐Dȩbowska, Katarzyna

doi:10.1016/j.jde.2014.12.022

Cited by 14 publications

(9 citation statements)

References 10 publications

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“…The key tool in our approach is the following generalization of the Miranda theorem Theorem 2.7 ( [18,19]). Let A i > 0, i = 1, .…”

Section: Theorem 26 ([7]mentioning

confidence: 99%

“…Besides, for the recent advances in other techniques for solving nonlinear problems resonant and non resonant. The generalized Miranda theorem (see [18,19]) can be applied to systems of ordinary differential equations, to both nonresonant and resonant cases. In [18] some examples of using this method for systems of differential equations of second order.…”

Section: Introductionmentioning

confidence: 99%

“…The generalized Miranda theorem (see [18,19]) can be applied to systems of ordinary differential equations, to both nonresonant and resonant cases. In [18] some examples of using this method for systems of differential equations of second order. In [21], the authors by means this method proved the existence of solutions for systems of differential equations of higher-order under non-resonant and resonant boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Solvability of two-point fractional boundary value problems at resonance

Baitiche¹,

Benbachir²,

Guerbati³

2020

Malaya J. Mat.

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“…The key tool in our approach is the following generalization of the Miranda theorem Theorem 2.7 ( [18,19]). Let A i > 0, i = 1, .…”

Section: Theorem 26 ([7]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solvability of two-point fractional boundary value problems at resonance

Baitiche¹,

Benbachir²,

Guerbati³

2020

Malaya J. Mat.

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“…As preparation for analyzing the existence of steady states in our model, we briefly recall some classical results by Poincaré and others. See [13,17,29,31] for detailed accounts of the relevant theory. In 1817, Bolzano proved the following well-known theorem.…”

Section: Technical Tool: the Poincaré-miranda Theoremmentioning

confidence: 99%

A two-patch epidemic model with nonlinear reinfection

Calvo

Hernández

Porter

et al. 2019

RMTA

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The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative example, we examine interactions between urban and rural populations on the dynamics of disease spreading. Using a compartmental framework of susceptible–infected susceptible (SIS) dynamics with some level of immunity, we formulate a model that allows non linear reinfection. We investigate the effects of population movement in a simple scenario: a case with two patches, which allows us to model population movement between urban and rural areas. To study the dynamics of the system, we compute a basic reproduction number for each population (urban and rural). We also compute steady states, determine the local stability of the disease-free steady state, and identify conditions for the existence of endemic steady states. From our analysis and computational experiments, we illustrate that population movement plays an important role in disease dynamics. In some cases, it can be rather beneﬁcial, as it can enlarge the region of stability of a disease-free steady state.

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“…(1.1) in finite-dimensional Banach spaces, including the method of upper and lower solutions [6,10,13], and degree theory and fixed point theory [8,12]. In this sense, in [20], the author gave a generalization of Miranda-Poincaré theorem and using this generalization proved theorems about the 0123456789(). : V,-vol existence for systems of k equations x = f (t, x, x ), where f : [0, 1] × R k × R k → R k is a vector function, subject to various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Periodic Solutions to Second-Order Nonlinear Differential Equations in Banach Spaces

Ariza-Ruiz

Garcia-Falset

2022

Mediterr. J. Math.

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In this article, we deal with the existence of solutions for the following second-order differential equation: $$\begin{aligned} \left\{ \begin{aligned}&u''(t)=f(t,u(t))+h(t)\\&u(a)-u(b)= u'(a)-u'(b)=0, \end{aligned}\right. \end{aligned}$$ u ′ ′ ( t ) = f ( t , u ( t ) ) + h ( t ) u ( a ) - u ( b ) = u ′ ( a ) - u ′ ( b ) = 0 , where $${\mathbb {B}}$$ B is a reflexive real Banach space, $$f:[a,b]\times {\mathbb {B}}\rightarrow {\mathbb {B}}$$ f : [ a , b ] × B → B is a sequentially weak–strong continuous mapping, and $$h:[a,b]\rightarrow {\mathbb {B}}$$ h : [ a , b ] → B is a continuous function on $${\mathbb {B}}.$$ B . The proofs are obtained using a recent generalization of the well-known Bolzano–Poincaré–Miranda theorem to infinite-dimensional Banach spaces. In the last section, we present three examples of application of the general result.

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On a generalization of the Miranda Theorem and its application to boundary value problems

Cited by 14 publications

References 10 publications

Solvability of two-point fractional boundary value problems at resonance

Solvability of two-point fractional boundary value problems at resonance

A two-patch epidemic model with nonlinear reinfection

Periodic Solutions to Second-Order Nonlinear Differential Equations in Banach Spaces

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