In this work we study the existence of a positive solutions to the non homogeneous equation ∆(|∆u|p−2∆u) = m|u|q−2u with Navier boundary conditions, where 1 < p, q < p2 and m ∈ L∞(Ω) \ {0}, m ≥ 0. In the case p > q and m ∈ C(Ω), we prove the uniqueness of this solution.

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

The state-dependent delay differential equation ẋ(t)+ m ∑ i=1 pi(t)x ( t − (Hix)(t) )= f (t), t ∈ [0,∞), x(ξ)= φ(ξ), ξ < 0, with state-dependent impulses is under consideration. Sufficient conditions for positivity of solutions to the Cauchy and periodic problems as well as conditions for positivity of solutions to the problem with a condition on the right end of the interval [0,ω] are given. S...

( ) ( ) ( ) 2 22 21 f t y a t x a t y + + = & (1) where x(t) and y(t) are two dynamic variables, aij are given constants and i f are constant forcing functions and they may take the form of a once-and-for-all exogenous shift from one constant level to the other. The solution to the above system will be two functions x(t) and y(t) that satisfy (1) and will consist of the general solution related...

In this paper, we present an extension of \G-networks" which includes queues with network state-dependent service rate, routing intensities and triggered batch signal movement. We prove that these networks have a geometric product form invariant measure. We establish su cient conditions for the existence of a solution to tra c equations.

Abstract   In vibratory systems, linear and nonlinear vibration absorbers can be used to suppress the primary and super-harmonic resonance responses. In this paper, the behavior of a nonlinear system with a nonlinear absorber, under the primary and super-harmonic resonances is investigated. The stiffnesses of the main system and the absorber are cubically nonlinear and the dampers are linear. M...

We introduce a ultradiscretization with parity variables of the q-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of q-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the parity variables. We study some solutions of the ultradiscrete Riccati-type equation and those o...

For the Euler equations in a thin domain Qε = Ω×(0, ε), Ω a rectangle in R, with initial data in (W (Qε)), q > 3, bounded uniformly in ε, the classical solution is shown to exist on a time interval (0, T (ε)), where T ( ) → +∞ as → 0. We compare this solution with that of a system of limiting equations on Ω.

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has ...

Here, a two server queueing system with Poisson arrivals and two different types of customers (M/H2/2 queue) is analyzed. A novel straightforward method is presented to acquire the exact and explicit forms of the performance measures. First, the steady state equations along with their Z-transforms are derived for the aforementioned queueing system. Using some limiting behaviors of the steady-st...