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.

Bounding Surfaces and Second Order Quasilinear Equations with Compatible Nonlinear Functional Boundary Conditions

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Jean Mawhin ◽  
Bevan Thompson
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Existence Results ◽  
Quasilinear Equations ◽  
Nonlinear Functional ◽  
Special Cases ◽  
Functional Boundary ◽  
Functional Boundary Conditions ◽  
Bounding Surfaces

AbstractWe establish existence results for solutions to functional boundary value problems for φ- Laplacian ordinary differential equations assuming there are lower and upper solutions and Lipschitz bounding surfaces for the derivative which we adapt to our problem. Our results apply to some problems which do not satisfy Nagumo growth bounds. Moreover they contain as special cases many results for the p- and ɸ-Laplacians as well as many results where the boundary conditions depend on n-points or even functionals. Our boundary conditions generalize those of Fabry and Habets, Cabada and Pouso, Cabada, O’Regan and Pouso, and many others.

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