In the present paper, a new method is developed to study the existence of an almost periodic solution for the ordinary or functional differential equations. The approaches are based on topological degree and novel estimation techniques for the a priori bounds of unknown solutions for Lx = λNx. To investigate the existence of an almost periodic solution, a few good methods have been presented in...

In this contribution Newton techniques based on Numerical Differentiation (ND), Direct Approach (DA) and Difference Matrix (DM) procedures are applied for the computation of the periodic steady state solution of single phase nonlinear electric networks containing magnetizing branches of transformers and alternating current arc furnaces. The results obtained with the Newton methods are compared ...

A new transition mechanism to Alfvén chaos via boundary crisis is reported. This crisis appears in a complex plasma region in the presence of a large number of coexisting attractors. We characterize an example of double boundary crises using the unstable periodic orbit determined from the numerical solution of the driven-dissipative derivative nonlinear Schrödinger equation, and demonstrate how...

The method of quasilinearization of Bellman and Kalaba [2] has been extended, refined, and generalized when the forcing function is the sum of a convex and concave function using coupled lower and upper solutions. This method is now known as the method of generalized quasilinearization. It has all the advantages of the quasilinearization method such that the iterates are solutions of linear sys...

We study the problem of finding a time-periodic solution to Euler–Bernoulli quasilinear equation describing vibrations beam subject stretching along horizontal axis. The boundary conditions correspond case rigidly clamped and elastically fixed endpoints. nonlinear term is power growth. Using variational method, we establish existence an unbounded sequence periodic solutions.

this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...

the numerical methods are of great importance for approximating the solutions of nonlinear ordinary or partial differential equations, especially when the nonlinear differential equation under consideration faces difficulties in obtaining its exact solution. in this latter case, we usually resort to one of the efficient numerical methods. in this paper, the chebyshev collocation method is sugge...

In this paper we present sufficient conditions for the existence of solutions to the periodic fourth order boundary value problem u(x) = f(x, u(x), u′(x), u′′(x), u′′′(x)) u(a) = u(b), i = 0, 1, 2, 3, for x ∈ [a, b], and f : [a, b] × R4 → R a continuous function. To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations w...

We provide a simple proof of the existence of dark solitons of the defocusing cubic nonlinear Schrödinger equation with periodic inhomogeneous nonlinearity. Moreover, our proof allows for a broader class of inhomogeneities and gives some new properties of the solutions. We also apply our approach to the defocusing cubic-quintic nonlinear Schrödinger equation with a periodic potential. We consid...