Coupled systems of Hammerstein-type integral equations with sign-changing kernels

Sousa, Robert de; Minhós, Feliz

doi:10.1016/j.nonrwa.2019.05.011

Cited by 9 publications

(10 citation statements)

References 22 publications

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“…Here we discuss in detail the existence and non-existence of positive solutions of the system (1.7), illustrating how the constants that occur in our theory can be computed or estimated. Our results are new and complement the ones in [1,4,15,16,[19][20][21].…”

Section: Introductionsupporting

confidence: 86%

“…The case of higher-order dependence within the equation has been in investigated recently, by means of the classical Krasnosel'skiȋ's theorem of cone compression-expansion, by de Sousa & Minhós [15]. In particular, de Sousa & Minhós [15] consider the existence of non-trivial solutions for the system of Hammerstein equations As an interesting application of their theory, de Sousa and Minhós apply their result to a system of BVPs of the form…”

Section: Introductionmentioning

confidence: 99%

“…The system (1.7) can be used as a model of the displacement of simply supported suspension bridge. In this model, the fourth-order equation describes the road bed and the second-order equation models the suspending cables, we refer to [15] for more details. On the other hand, the case of equations of the form…”

Section: Introductionmentioning

confidence: 99%

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Positive solutions of systems of perturbed Hammerstein integral equations with arbitrary order dependence

Infante

2021

Phil. Trans. R. Soc. A.

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Motivated by the study of systems of higher-order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral equations, where the nonlinearities and the functionals involved depend on some derivatives. We improve and complement earlier results in the literature. We also provide some examples in order to illustrate the applicability of the theoretical results. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

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Section: Introductionsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Positive solutions of systems of perturbed Hammerstein integral equations with arbitrary order dependence

Infante

2021

Phil. Trans. R. Soc. A.

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“…Second, we apply the new coexistence fixed point theorems to invigilate the existence of at lease one nonnegative coexistence solutions of systems of Hammerstein integral equations of the form

z_{i} false(x false) = true \int_{0}^{1} k_{i} false(x, s false) f_{i} false(s, boldz false(s false) false) d s for each x \in false[0,1 false] and i \in I_{n},

where

f_{i} : false[0,1 false] \times ℝ_{+}^{n} \to ℝ_{+}

satisfies the Carathéodory conditions on

false[0,1 false] \times ℝ_{+}^{n}

. The existence of nonzero nonnegative solutions of the system () and systems of perturbed Hammerstein integral equations have been widely studied, for example, in previous studies 3,7‐16 . These existence results imply that the nonzero nonnegative solutions z satisfy z i ≠ 0 for some i ∈ I n , but they cannot justify whether the nonzero nonnegative solutions are coexistence solutions, that is, z i ≠ 0 for each i ∈ I n .…”

Section: Introductionmentioning

confidence: 99%

Coexistence fixed point theorems in product Banach spaces and applications

Lan

2020

Math Methods in App Sciences

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New coexistence fixed point theorems in product Banach spaces are established via the classical theory of fixed point index for compact maps defined on cones. Each component of a coexistence fixed point is nonzero. These coexistence fixed point theorems are applied to obtain results on coexistence solutions of systems of Hammerstein integral equations, second‐order ordinary differential equations with general separated boundary conditions, and one‐dimensional competition model of Ricker types.

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“…Lidstone-type boundary value problems have applications in real phenomena such as the study of bending of simply-supported beams or suspended bridges (see [13,14]). In [8], de Sousa and Minhós used Lidstone boundary conditions in a coupled system composed by two and fourth order differential equations, to model the bending of the main beam in suspension bridges. Likewise, Li and Gao [15], discuss models of a static bending elastic beam whose two ends are simply supported, given by Lidstone-type boundary conditions.…”

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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Coupled systems of Hammerstein-type integral equations with sign-changing kernels

Cited by 9 publications

References 22 publications

Positive solutions of systems of perturbed Hammerstein integral equations with arbitrary order dependence

Positive solutions of systems of perturbed Hammerstein integral equations with arbitrary order dependence

Coexistence fixed point theorems in product Banach spaces and applications

On Coupled Systems of Lidstone-Type Boundary Value Problems

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