In this paper, we have presented a finite difference technique to solve singularly perturbed two-point boundary value problem using deviating argument. We have replaced the given second order boundary value problem by an asymptotically equivalent first order differential equation with deviating argument. We have applied a fourth order finite difference approximation for the first derivative and...

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...

and Applied Analysis 3 Motivated by 14, 15 , here we study the existence of AL-solutions for 1.1 . The approach is completely different from the one used in 15 , in which an iteration process, jointly with a comparison with the linear equation y 4 q t y 2 0, is employed. Our tools are based on a topological method, certain integral inequalities, and some auxiliary functions. In particular, for ...

By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian generalized Liénard equation with deviating argument (φp(x′(t)))′ + f(t, x(t))x′(t) + β(t)g(x(t− τ(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.

By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian Liénard equation with a deviating argument (φp(x′(t)))′ + f(x(t))x′(t) + g(x(t− τ(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.