WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 18, 2019
The Number of Solutions to the Boundary Value Problem for the Second Order Differential Equation with Cubic Nonlinearity
Author:
Abstract: The differential equation with cubic nonlinearity x' = -αx + b(x^3) is considered together with the Sturm - Liouville type boundary conditions. The number of solutions for the Sturm - Liouville boundary value p roblem is given. The equation for the initial values of solutions to boundary value problem is derived using representation by Jacobian elliptic functions. An explanatory example is given with a number of visualizations.