The Strong Nonlinear Limit-Point/Limit-Circle Problem

The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations. This concept was extended to second-order nonlinear equations in the late 1970's and later, to higher order nonlinear equations. This monograph traces the development of what is known as the strong nonlinear limit-point and limit-circle properties of solutions. In addition to bringing together all such results into one place, some new directions that the study has taken as well as some open problems for future research are indicated.
Contents: The Origins of the Limit-Point/Limit-Circle ProblemEquations with p-LaplacianStrong Limit-Point/Limit-Circle PropertiesDamped EquationsHigher Order EquationsDelay Equations IDelay Equations IITransformations of the Basic EquationNotes, Open Problems, and Future Directions
Readership: Graduate students and researchers of mathematics integrated in limit-point/limit circle topics.
Keywords:Limit-Point Problem;Limit-Circle Problem;Strong Limit-Point Problem;Strong Limit-Circle Problem;Asymptotic Properties of Solutions;Nonlinear Differential Equations;Second Order Equations;Higher Order EquationsReview:Key Features:There is no other source of results on this problem except for the individual papers that appear in the literature. This work collects all that is known about this problem in one placeThe references on the nonlinear problem are complete up to 2017Directions for future research are indicated