Theory of impulsive partial differential equations can be applied to many fields, such as to biology, population growth, engineering, generic repression, control theory and climate model. In the last few years, the fundamental theory of partial differential equations with impulses has undergone intensive development. The qualitative theory of this class of equations, however, is still in an ini...

We obtain some oscillation criteria for solutions of the nonlinear delay difference equation of the form xn+1−xn+pn ∏m j=1x αj n−kj = 0. 2000 Mathematics Subject Classification. 39A10.

In this paper, Newton Harmonic Balance Method (NHBM) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. Periodic solution is analytically verified and consequently the relation between the Natural Frequency and the amplitude is obtained in an ana...

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

Sufficient conditions for the oscillation of the nonlinear second order differential equation (a(t)x) +Q(t, x) = P (t, x, x) are established where the coefficients are continuous and a(t) is nonnegative.

The field of nonlinear optics has developed rapidly since its beginning in 1961. This development is in both the theory of nonlinear effects and the theory of nonlinear interactions in solids, and in the applications of nonlinear devices. This review discusses nonlinear interactions in solids and the resultant nonlinear coupling of electromagnetic waves that leads to second harmonic generation,...

In this paper, we study oscillatory properties of solutions for the nonlinear impulsive hyperbolic equations with several delays. We establish sufficient conditions for oscillation of all solutions.

An important consideration in control issues is control of nonlinear systems. Sliding control is among those nonlinear controllers that can control the system desirably in the presence of unstructured uncertainties of carelessness in specifying parameters of the system. In sliding control, also called Variable Structure Control, the main objectives of the controller &#10are achieved by introduc...

An important consideration in control issues is control of nonlinear systems. Sliding control is among those nonlinear controllers that can control the system desirably in the presence of unstructured uncertainties of carelessness in specifying parameters of the system. In sliding control, also called Variable Structure Control, the main objectives of the controller are achieved by introducin...