In this paper we establish the existence of the uniform attractor for a semi linear parabolic problem with bounded non autonomous disturbances in the phase space of continuous functions. We applied obtained results to prove the asymptotic gain property with respect to the global attractor of the undisturbed system.
We investigate the problem with perturbed periodic boundary values with for some arbitrary positive real number , by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients , and which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon that all...
We establish new conjugacy criteria for half-linear second order differential equations. These criteria are based on the relationship between conjugacy of the investigated equation and nonpositivity of the associated energy functional.
Picone identity for a class of nonlinear differential equations is established and various qualitative results (such as Wirtinger-type inequality and the existence of zeros of first components of solutions) are obtained with the help of this new formula.
For initial value problem (IVPs) in ordinary second order differential equations of the special form possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to...