If V is in L, virtually any perturbation technique allows one to control u (and, in fact, to show that all solutions of (1) are bounded as x → ∞). We are interested in cases where V is not L but is small at infinity in some sense. We want to generalize what has turned out to be a powerful set of tools in case V0 ≡ 0, namely, the use of modified Prüfer equations and their discrete analogs, which...

In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators. Keywords—Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators

In this paper, we have applied the homotopy perturbation method (HPM) for obtaining the analytical solution of unsteady flow of gas through a porous medium and we have also compared the findings of this research with some other analytical results. Results showed a very good agreement between results of HPM and the numerical solutions of the problem rather than other analytical solutions which h...

in this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. the system is firstly, transformed into an ordinary differential equation by wave transformation. the solution of ode is obtained by the homotopy perturbation method. to show the periodic behavior of the solution, a modification based on the laplace transforms and...