Nonlinear Hammerstein integral equations via local linking and mountain pass

2011 ◽  
Vol 60 (3) ◽  
pp. 357-364
Author(s):  
Donal O’Regan
Keyword(s):  
Integral Equations ◽  
Mountain Pass ◽  
Local Linking ◽  
Hammerstein Integral 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.

scholarly journals Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets

2005 ◽  
Vol 2005 (1) ◽  
pp. 113-121 ◽  
Author(s):  
M. Lakestani ◽  
M. Razzaghi ◽  
M. Dehghan
Keyword(s):  
Integral Equations ◽  
Algebraic Equations ◽  
B Spline ◽  
Compactly Supported ◽  
Hammerstein Integral Equations ◽  
Spline Wavelets

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through an illustrative example.

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