Anita Kirichuka, "The Number of Solutions to the Boundary Value Problem for the Second Order Differential Equation with Cubic Nonlinearity," WSEAS Transactions on Mathematics, vol. 18, pp. 230-236, 2019, DOI:
Anita Kirichuka. The Number of Solutions to the Boundary Value Problem for the Second Order Differential Equation with Cubic Nonlinearity.
WSEAS Transactions on Mathematics. 2019;18:230-236.
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.
Keywords:
Boundary value problem, cubic nonlinearity, phase trajectory, multiplicity of solutions, Jacobian elliptic function
Pages: 230-236 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #31 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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