WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 18, 2023
On Boundary Value Problems for Liénard Type Equation
Authors: ,
Abstract: The generalized Liénard type differential equation is studied together with the two-point linear boundary conditions of the Sturm-Liouville type. The existence and multiplicity of solutions are considered. The existence under suitable conditions is shown to follow from the lower and upper functions theory. For multiplicity, the polar coordinates approach is used. The multiplicity results are based on the comparison between behavior of solutions near the trivial one, and solutions near the special one, which is preassumed to be non-oscillatory. The existence of the latter is required. It is shown also, that these conditions are fulfilled for a relatively broad class of equations. Some examples are constructed, which are supplied by comments and illustrations.
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Keywords: Ordinary differential equations, multiple solutions, existence of solutions, Liénard type equations, phase portrait, oscillatory behaviors, boundary value problems, variational equations, heteroclinic trajectories, homoclinic trajectories
Pages: 437-443
DOI: 10.37394/23203.2023.18.47