Anita Kirichuka, Felix Sadyrbaev, "Multiple Solutions for Lie´nard Type Generalized Equations," WSEAS Transactions on Systems, vol. 22, pp. 578-583, 2023, DOI:10.37394/23202.2023.22.58
Anita Kirichuka, Felix Sadyrbaev. Multiple Solutions for Lie´nard Type Generalized Equations.
WSEAS Transactions on Systems. 2023;22:578-583. 10.37394/23202.2023.22.58
WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 22, 2023
Multiple Solutions for Lie´nard Type Generalized Equations
Authors: ,
Abstract: Two-point boundary value problems for second-order ordinary differential equations of Lie´nard type are studied. A comparison is made between equations x´´ + f (x) x´2 + g(x) = 0 and x´´ + f (x) x´ + g(x) = 0. In our approach, the Dirichlet boundary conditions are considered. The estimates of the number of solutions in both cases are obtained. These estimates are based on considering the equation of variations around the trivial solution and some additional assumptions. Examples and visualizations are supplied.
Keywords:
Lie´nard equation, ordinary differential equation, phase plane, boundary value problems, multiplicity of solutions, number of solutions
Pages: 578-583 WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 22, 2023, Art. #58 DOI: 10.37394/23202.2023.22.58
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