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.

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 Nonnegative solutions for a heterogeneous degenerate competition model

2004 ◽  
Vol 46 (2) ◽  
pp. 273-297 ◽  
Author(s):  
Antonio Suárez
Keyword(s):  
Fixed Point ◽  
Positive Solution ◽  
Nonlinear Diffusion ◽  
Fixed Point Index ◽  
Competition Model ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Qualitative Properties ◽  
Nonnegative Solutions ◽  
Monotonicity Methods

AbstractThis paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as the uniqueness of a positive solution. In order to obtain these results we employ monotonicity methods, singular spectral theory and a fixed point index.

scholarly journals Positive Fixed Points for Semipositone Operators in Ordered Banach Spaces and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Zengqin Zhao ◽  
Xinsheng Du
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Fixed Point Index ◽  
Index Theorem ◽  
Point Index ◽  
Hammerstein Integral Equations ◽  
Polynomial Type ◽  
Fixed Point Index Theorem ◽  
Abstract Spaces ◽  
Ordered Banach Spaces

The theory of semipositone integral equations and semipositone ordinary differential equations has been emerging as an important area of investigation in recent years, but the research on semipositone operators in abstract spaces is yet rare. By employing a well-known fixed point index theorem and combining it with a translation substitution, we study the existence of positive fixed points for a semipositone operator in ordered Banach space. Lastly, we apply the results to Hammerstein integral equations of polynomial type.

A fixed point index for maps with Borsuk-presentable fixed point set

1982 ◽  
Vol 38 (1) ◽  
pp. 549-555
Author(s):  
Christian C. Fenske
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Point Index ◽  
Fixed Point Set ◽  
Point Set

scholarly journals Fixed point index and decompositions of isolated invariant compacta

2004 ◽  
Vol 141 (1-3) ◽  
pp. 207-223
Author(s):  
Francisco R. Ruiz del Portal ◽  
José M. Salazar
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Point Index
Sign in / Sign up

Export Citation Format

Share Document