Sharif Digital Repository

In this paper, we consider the solution of an nth order boundary-value problem. We solve this problem by changing the problem to a system of two integral-differential equations and using the variational iteration method. By giving three examples and comparing with the other methods, the efficiency of the method will be shown. © 2007 Elsevier Inc. All rights reserved  

We prove under quite general assumptions the existence of a bounded positive solution of the semilinear Schrödinger equation Δ u + f (x, u) = 0 in a two-dimensional exterior domain. Our results are independent of the behavior of f (x, u) when u is sufficiently small or sufficiently large and just require some knowledge about the nonlinearity f (x, u) for a ≤ u ≤ b, for some a, b > 0. We obtain solutions with a prescribed positive lower bound. © 2007 Elsevier Ltd. All rights reserved  

We consider the generalized Liénard systemfrac(d x, d t) = frac(1, a (x)) [h (y) - F (x)],frac(d y, d t) = - a (x) g (x), where a, F, g, and h are continuous functions on R and a (x) > 0, for x ∈ R. Under the assumptions that the origin is a unique equilibrium, we study the problem whether all trajectories of this system intersect the vertical isocline h (y) = F (x), which is very important in the global asymptotic stability of the origin, oscillation theory, and existence of periodic solutions. Under quite general assumptions we obtain sufficient and necessary conditions which are very sharp. Our results extend the results of Villari and Zanolin, and Hara and Sugie for this system with h... 

In this paper we consider a nonlinear parabolic equation with gradient dependent nonlinearities of the form ut - Δu = a|u|p + b| ▽ u|q, 0 < p, q and a, b ∈ ℝ, with homogeneous boundary condition in a bounded domain Ω ⊆ ℝN. In the case 0 < p, g ≤ 1 we prove the existence of solution for suitable initial data. A comparison theorem for the solutions with respect to supersolutions and subsolutions is proved. Using these result, uniqueness and boundedness of solutions is studied  

The existence of travelling wave solution to equations of a viscous heat conducting combustible fluid is proved. The reactions are assumed to be one step exothermic reactions with a natural discontinuous reaction rate function. The problem is studied for a general gas. Instead of assuming the ideal gas conditions we consider a general thermodynamics which is described by a fairly mild set of hypotheses. Travelling waves for detonations reduce to specific heteroclinic orbits of a discontinuous system of ODE's. The existence proof for heteroclinic orbits corresponding to weak and strong detonation waves is carried out by some general topological arguments in ODE. The uniqueness and... 

The existence of travelling wave solutions to equations of a viscous, heat-conducting combustible fluid is proved. The reactions are assumed to be one step exothermic reactions with a natural discontinuous reaction rate function. The problem is studied for a general gas. Instead of assuming the ideal gas conditions we consider a general thermodynamics which is described by a fairly mild set of hypotheses. The existence proof of travelling waves for Chapman-Jouguet detonation reduces to finding specific heteroclinic orbits of a discontinuous system of ordinary differential equations; these heteroclinic orbits connect a rest point corresponding to unburnt state to that of the burnt state. The... 

In this paper we study the problem of the existence of limit cycles for a predator-prey system with a functional response. From the ecological point of view, the existence of a limit cycle shows the oscillatory behaviour of the populations. A necessary and sufficient condition for the existence of limit cycles when the derivative of the functional response is positive, decreasing, and concave upward is given. Global stability of the system can be established by our results. In addition it is shown that the local stability and global stability of the critical point of the system are equivalent. The results cover most of the models which have been proposed in the ecological literature for...