The mixed BVP for second order nonlinear ordinary differential equation at resonance

Efficient sufficient conditions are established for the solvability of the mixed problem where in the case where the homogeneous linear problem has nontrivial solutions.     

Oscillating solutions of a nonlinear fourth order ordinary differential equation

We study the existence of periodic solutions for a nonlinear fourth order ordinary differential equation. Under suitable conditions we prove the existence of at least one solution of the problem applying coincidence degree theory and the method of upper and lower solutions.     

On the numerical solution of second order ordinary differential equations in the high-frequency regime

We describe an algorithm for the numerical solution of second order linear ordinary differential equations in the high-frequency regime. It is based on the recent observation that solutions of equations of this type can be accurately represented using nonoscillatory phase functions. Unlike standard solvers for ordinary differential equations, the running time of our algorithm is independent of the frequency of oscillation of the solutions. We illustrate this and other properties of the method with several numerical experiments.     

Some oscillation criteria for second order nonlinear functional ordinary differential equations

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) ＞ 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.     

On oscillation of nonlinear second order differential equation with damping term

In this paper we investigate the oscillation of nonlinear differdntial equation with damping term. Some new oscillation criteria for the equation are obtained.     

On a nonlinear distributed order fractional differential equation

We study the existence and the uniqueness of mild and classical solutions for a class of equations of the form . Such equations arise in distributed derivatives models of viscoelasticity and system identification theory. We also formulate a variational principle for a more general equation based on a method of doubling of variables for such equations.     

Generalized quasilinearization method for a second order ordinary differential equation with Dirichlet boundary conditions

We study the existence and approximation of solutions for a nonlinear second order ordinary differential equation with Dirichlet boundary value conditions. We present a generalized quasilinearization technique to obtain a sequence of approximate solutions converging quadratically to a solution.

     

The first boundary-value problem for a singular nonlinear ordinary differential equation of fourth order

The solvability of the boundary-value problem

Periodic solutions of a nonlinear second order differential equation with delay

It is proved that the autonomous difference-differential equation

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(0) has, for a broad class of functions f, a nonconstant periodic solution whenever the associated characteristic equation has a root with positive real part.     

Subfunctions for second order ordinary differential equations

Explicit upper and lower bounds are constructed for a functional defined on the difference of solutions to a class of nonlinear hyperbolic problems modelling string vibrations. Such bounds indicate how solutions are affected by the input data over a finite time interval. The logarithmic convexity method is used to obtain two second order ordinary differential inequalities for the appropriate functional. These inequalities are then related to two systems of first order equations whose solutions are the desired bounds.