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.

We consider the problem of nding a solution of a nonlinear system of equations subject to some box constraints. To this end, we introduce a new active set-type Newton method with global and local fast convergence properties. The method generates feasible iterates and has to solve only one linear system of equations at each iteration. Due to our active set strategy, this linear system is of redu...

Pollution has become a very serious threat to our environment. Monitoring pollution is the rst step toward planning to save the environment. The use of dierential equations, monitoring pollution has become possible. In this paper, a Ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. The method is based upon Bernoul...

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...

The aim of this paper is to present algebraic method which is called Wu's method to solving fuzzy complex systems of linear equations. Wu's method is used as a solution procedure for solving the crisp polynomial equations system. This algorithm leads to solving characteristic sets that are amenable to easy solution. To illustrate the easy application of the proposed method, numerical examples a...

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...