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

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190376
Author(s):  
Gennaro Infante
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Difference Equations ◽  
Arbitrary Order ◽  
Theme Issue ◽  
Topological Methods ◽  
Hammerstein Integral Equations ◽  
Functional Boundary ◽  
Functional Boundary Conditions ◽  
Theoretical Results

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’.

scholarly journals Nontrivial Solutions of Systems of Perturbed Hammerstein Integral Equations with Functional Terms

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 330
Author(s):  
Gennaro Infante
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integral Equations ◽  
General Class ◽  
Fixed Point Index ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Hammerstein Integral Equations ◽  
Functional Boundary ◽  
Functional Boundary Conditions

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the components of the system and their derivatives. The results are applicable to systems of nonlocal second order ordinary differential equations subject to functional boundary conditions, this is illustrated in an example. Our approach is based on the classical fixed point index.

Degree, quaternions and periodic solutions

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190378
Author(s):  
Jean Mawhin
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Topological Degree ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Brouwer Degree ◽  
Homogeneous Polynomials ◽  
Theme Issue ◽  
Existence And Multiplicity

The paper computes the Brouwer degree of some classes of homogeneous polynomials defined on quaternions and applies the results, together with a continuation theorem of coincidence degree theory, to the existence and multiplicity of periodic solutions of a class of systems of quaternionic valued ordinary differential equations. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

scholarly journals Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2267
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la De la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Control Function ◽  
Cone Metric Spaces ◽  
Tripled Fixed Point ◽  
Contractive Type ◽  
Theoretical Results ◽  
Cone Metric

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

scholarly journals Numerical solvability of a class of Volterra-Hammerstein integral equations with noncompact kernels

2005 ◽  
Vol 2005 (2) ◽  
pp. 171-181 ◽  
Author(s):  
M. Hadizadeh ◽  
M. Mohamadsohi
Keyword(s):  
Integral Equations ◽  
Singular Integral Equations ◽  
Nonlinear Functions ◽  
Product Integration ◽  
Existence And Uniqueness Results ◽  
Hammerstein Integral Equations ◽  
Uniqueness Results ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations ◽  
Theoretical Results

We study the numerical solvability of a class of nonlinear weakly singular integral equations of Volterra-Hammerstein type with noncompact kernels. We obtain existence and uniqueness results and analyze the product integration methods for these equations under some verifiable conditions on the kernels and nonlinear functions. The convergence analysis is investigated and finally numerical experiments are given, which confirm our theoretical results.

scholarly journals Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hasanen A. Hammad ◽  
Hassen Aydi ◽  
Nabil Mlaiki
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Integral Operators ◽  
Volterra Integral Equations ◽  
Fractional Integrals ◽  
Uniqueness Of Solutions ◽  
Mild Conditions ◽  
Contractive Type ◽  
Theoretical Results

AbstractIn this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, $\eta _{\gimel }^{\nu }$ η ℷ ν -metric spaces) are obtained. Moreover, some related consequences dealing with a common fixed point concept and nontrivial examples to support our results are presented. Ultimately, we use the theoretical results to discuss the existence and uniqueness of solutions of 2D Volterra integral equations, Riemann–Liouville integrals and Atangana–Baleanu integral operators are given.

scholarly journals A Unique Coupled Common Fixed Point Theorem for Symmetric(φ,ψ)-Contractive Mappings in OrderedG-Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Manish Jain ◽  
Kenan Taş
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Common Fixed Point ◽  
Contractive Mappings ◽  
Theoretical Results ◽  
Common Fixed Point Theorem

We establish the existence and uniqueness of coupled common fixed point for symmetric(φ,ψ)-contractive mappings in the framework of orderedG-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011), Nashine (2012), and Mohiuddine and Alotaibi (2012), thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.

scholarly journals Nonzero Positive Solutions of Elliptic Systems with Gradient Dependence and Functional BCs

2020 ◽  
Vol 20 (4) ◽  
pp. 911-931 ◽  
Author(s):  
Stefano Biagi ◽  
Alessandro Calamai ◽  
Gennaro Infante
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence Result ◽  
Elliptic Systems ◽  
Existence Results ◽  
Topological Methods ◽  
Elliptic Differential Equations ◽  
Nonnegative Solutions ◽  
Functional Boundary ◽  
Functional Boundary Conditions

AbstractWe discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results.

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