We consider a singular elliptic perturbation of a Hammerstein integral equation with singular nonlinear term at the origin. The compactness of the solutions to the perturbed problem and, hence, the existence of a positive solution for the integral equation are proved. Moreover, these results are applied to nonlinear singular homogeneous Dirichlet problems.

A wavelet collocation method for nonlinear Hammerstein equations is formulated. A sparsity in the Jacobian matrix is obtained which gives rise to a fast algorithm for nonlinear solvers such as the Newton’s method and the quasi-Newton method. A fast multilevel augmentation method is developed on a transformed nonlinear equation which gives an additional saving in computational time.

Inverse fuzzy process model based direct adaptive control. [2] J. Abonyi and R. Babuška. Local and global identification and interpretation of parameters in Takagi–Sugeno fuzzy models. In Proceed-[3] J. Abonyi and R. Babuška. Local and global identification and interpretation of parameters in Takagi–Sugeno fuzzy models. In Proceed-tification and control of nonlinear systems using fuzzy Hammerst...

Nonlinear block-oriented systems, including the Hammerstein, Wiener and feedbacknonlinear systems have attracted considerable research interest both from the industrial and academic environments (Bai, 1998), (Greblicki, 1989), (Latawiec, 2004), (Latawiec et al., 2003), (Latawiec et al., 2004), (Pearson & Pottman, 2000). It is well known that orthonormal basis functions (OBF) (Bokor et al., 1999...

In this paper‎, ‎existence of an $L^p$-solution for 2DIEs (Two‎ ‎Dimensional Integral Equations) of the Hammerstein type is‎ ‎discussed‎. ‎The main tools in this discussion are Schaefer's and‎ ‎Schauder's fixed point theorems with a general version of‎ ‎Gronwall's inequality‎.

The aim of this note is to study convergence and convergence rates of the regularized solutions for the operator equation of Hammerstein type x + F2F1(x) = f in reflexive Banach spaces under the non-monotone perturbations F h 2 and F h 1 of the operators F2 and F1, respectively.

The nonlinear differential equation x" = f(t, x(t)), f being 22T-periodic in t, is considered for the existence of 27T-periodic solutions. The equation is reduced to an equivalent system of two Hammerstein equations. The case of nonlinear perturbation at resonance is also discussed.

In this paper, a generalization of Nadler’s fixed point theorem is presented for H-type k-multivalued weak contractive mappings. We consider a nonconvex Hammerstein type integral inclusion and prove an existence theorem by using an H-type multi-valued weak contractive mapping.

We developed a wrist model using neural networks based on Hammerstein cascade. The model can predict the wrist angle while stimulating by different pulse widths of the stimulation. It consists of neural networks to represent the muscle recruitment properties, and a linear dynamical system to represent the time variation. Simulation results on actual measurements were compared with the output fr...

In this paper we propose a new technique for the identification of NARX Hammerstein systems. The new technique is based on the theory of Least Squares Support Vector Machines function-approximation and allows to determine the memoryless static nonlinearity as well as the linear model parameters. As the technique is non-parametric by nature, no assumptions about the static nonlinearity need to b...