On Boundary Value Problems for Liénard Type Equation

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.