In this work, we deal with normalizable-balanced singular systems, that is, singular systems where the obtained closed-loop system is balanced by an appropriate feedback. In the invariant case, we use a proportional and derivative feedback to obtain systems without infinite poles. In addition, the existence and construction of state-feedbacks to obtain normalizable-balanced N-periodic singular ...

the extended homogeneous balance method is used to construct exacttraveling wave solutions of the maccari system, in which thehomogeneous balance method is applied to solve the riccati equationand the reduced nonlinear ordinary differential equation. many exacttraveling wave solutions of the maccari system equation aresuccessfully obtained.

We prove that one-dimensional Schrodinger operators with even almost periodic potential have no point spectrum for a dense Gδ in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense Gδ in Θ even if the frequency is an irrational with good Diophantine properties.

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

A singular perturbation problem from the artificial compressible system to incompressible is considered for a doubly diffusive convection when Hopf bifurcation motionless state occurs in system. It proved that also small parameter, called Mach number. The time periodic solution branch of shown converge corresponding bifurcating limit vanishing

This paper is concerned with a class of singular equations modeling the combustion of premixed gas in periodic media. The model involves two parameters: the period of the medium |L| and a singular parameter ε related to the activation energy. The existence of pulsating travelling fronts for fixed ε and |L| was proved by H. Berestycki and F. Hamel in [BH]. In the present paper, we investigate th...

In this work, N-periodic linear singular systems are considered. Feedbacks for obtaining positive N-periodic singular systems are analyzed. Some properties on the existence of these feedbacks are established. The concept of holdability of the setR+ is used for getting a positive trajectory of the closed-loop singular systems. This paper examines how feedbacks can be used to modify the trajector...