Bounded solutions of a nonlinear second order differential equation with asymptotic conditions modeling ocean flows

Second Order ◽

Bounded Solutions ◽

Order Ordinary Differential Equation ◽

Derivatives Of

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

The Rate of Growth of Solutions of a Second-Order Differential Equation

Journal of the Society for Industrial and Applied Mathematics ◽

10.1137/0110034 ◽

1962 ◽

Vol 10 (3) ◽

pp. 454-468 ◽

Cited By ~ 10

Author(s):

Eugene J. Putzer

Keyword(s):

Differential Equation ◽

Second Order ◽

Rate Of Growth ◽

Growth Of Solutions

Existence and uniqueness of solutions for a second order differential equation with integral boundary conditions

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.03.118 ◽

2010 ◽

Vol 216 (9) ◽

pp. 2718-2727 ◽

Cited By ~ 2

Author(s):

Youyu Wang ◽

Guofeng Liu ◽

Yinping Hu

Keyword(s):

Differential Equation ◽

Boundary Conditions ◽

Existence And Uniqueness ◽

Second Order Differential Equation

Integral Boundary Conditions ◽

Second Order ◽

Uniqueness Of Solutions ◽

Integral Boundary ◽

A mechanical method for the solution of second-order linear differential equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100009804 ◽

1931 ◽

Vol 27 (4) ◽

pp. 546-552 ◽

Cited By ~ 1

Author(s):

E. C. Bullard ◽

P. B. Moon

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Boundary Conditions ◽

Second Order ◽

Linear Differential Equations ◽

Mechanical Method ◽

Order Linear ◽

Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

Periodic solutions for periodic second-order differential equations with variable potentials

Journal of Applied Analysis ◽

10.1515/jaa-2018-0013 ◽

2018 ◽

Vol 24 (2) ◽

pp. 127-137

Author(s):

Jaume Llibre ◽

Ammar Makhlouf

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Periodic Solutions ◽

Sufficient Conditions ◽

Second Order ◽

Second Order Differential Equations ◽

Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

Journal of Applied Analysis ◽

10.1515/jaa-2017-0018 ◽

2017 ◽

Vol 23 (2) ◽

Author(s):

Muhad H. Abregov ◽

Vladimir Z. Kanchukoev ◽

Maryana A. Shardanova

Keyword(s):

Differential Equation ◽

Numerical Methods ◽

Finite Difference ◽

Boundary Value Problem ◽

Second Order Differential Equation

Boundary Value ◽

Sufficient Conditions ◽

Second Order ◽

Deviating Argument ◽

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.