Solutions of perturbed Hammerstein integral equations with applications

Cianciaruso, Filomena; Infante, Gennaro; Pietramala, Paolamaria

doi:10.1016/j.nonrwa.2016.07.004

Cited by 53 publications

(45 citation statements)

References 73 publications

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“…The case n = 1 has been studied recently by Goodrich [5,6], who complemented the earlier works [3,9]. In particular, Goodrich studied the equation The functional formulation (1.3) is well suited for handling, in a unified way, multi-point and integral BCs.…”

Section: Introductionmentioning

confidence: 99%

Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence

Infante¹

2020

Discrete &Amp; Continuous Dynamical Systems - B

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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.2010 Mathematics Subject Classification. Primary 45G15, secondary 34B10, 34B18, 47H30.

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Section: Introductionmentioning

confidence: 99%

Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence

Infante¹

2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…We also highlight recent works, not necessarily in real line or half-line, on Hammerstein-type integral equations, with several approaches and applications in References [13,[15][16][17][18][19][20][21][22] and the references therein.…”

Section: Introductionmentioning

confidence: 94%

Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line

Minhós

Sousa

2020

Mathematics

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In this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder's fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivatives on R, combined with the equiconvergence at ±∞ to recover the compactness of the correspondent operators. To the best of our knowledge, it is the first time where coupled Hammerstein-type integral equations in real line are considered with nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation. On the other hand, we emphasize that the kernel functions can change sign and their derivatives in order to the first variable may be discontinuous. The last section contains an application to a model to study the deflection of a coupled system of infinite beams.

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“…Hammerstein family of integral equations appears in some mathematical models, such as electrostatic drift waves and low-frequency electromagnetic perturbation (see [14]) and signal theory (see [19]). Other applications and very successful results can be found on [2,10,21] and the references therein.…”

Section: Introductionmentioning

confidence: 97%

On coupled systems of Hammerstein integral equations

Sousa¹,

Minhós²

2019

Bound Value Probl

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In this paper we deal with generalized coupled systems of integral equations of Hammerstein type with nonlinearities depending on several derivatives of both variables and we underline that both equations and both variables can have a different regularity. This detail is very important as it allows for the application to, for example, boundary value problems with coupled systems composed of differential equations of different orders and distinct boundary conditions. This issue will open a new field of applications to phenomena modeled by coupled systems requiring different types of regularity for the unknown functions. The arguments follow Guo-Krasnosel'skiȋ compression-expansion theory on cones and the kernel functions are nonnegative and verifying adequate sign and growth assumptions. The dependence of the derivatives is overcome by the construction of suitable cones taking into account certain conditions of sublinearity/superlinearity at the origin and at +∞.

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Solutions of perturbed Hammerstein integral equations with applications

Cited by 53 publications

References 73 publications

Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence

Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence

Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line

On coupled systems of Hammerstein integral equations

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