Search results for "Second order differential equations"
showing 5 items of 5 documents
Sliding solutions of second-order differential equations with discontinuous right-hand side
2017
We consider second-order ordinary differential equations with discontinuous right-hand side. We analyze the concept of solution of this kind of equations and determine analytical conditions that are satisfied by typical solutions. Moreover, the existence and uniqueness of solutions and sliding solutions are studied. Copyright © 2017 John Wiley & Sons, Ltd.
Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side
2012
Abstract The main goal of this paper is to discuss the existence of periodic solutions of the second order equation: y ″ + η sgn ( y ) = α sin ( β t ) with ( η , α , β ) ∈ R 3 η > 0 . We analyze the dynamics of such an equation around the origin which is a typical singularity of non-smooth dynamical systems. The main results consist in exhibiting conditions on the existence of typical periodic solutions that appear generically in such systems. We emphasize that the mechanism employed here is applicable to many more systems. In fact this work fits into a general program for understanding the dynamics of non-autonomous differential equations with discontinuous right-hand sides.
Indefinite integrals of special functions from hybrid equations
2019
Elementary linear first and second order differential equations can always be constructed for twice differentiable functions by explicitly including the function's derivatives in the definition of ...
Global Non-monotonicity of Solutions to Nonlinear Second-Order Differential Equations
2018
We study behavior of solutions to two classes of nonlinear second-order differential equations with a damping term. Sufficient conditions for the first derivative of a solution x(t) to change sign at least once in a given interval (in a given infinite sequence of intervals) are provided. These conditions imply global non-monotone behavior of solutions.
Indefinite integrals from Wronskians and related linear second-order differential equations
2021
Many indefinite integrals are derived for Bessel functions and associated Legendre functions from particular transformations of their differential equations which are closely linked to Wronskians. A large portion of the results for Bessel functions is known, but all the results for associated Legendre functions appear to be new. The method can be applied to many other special functions. All results have been checked by differentiation using Mathematica.