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This selfcontained monograph traces the evolution of the limitpoint/limitcircle problem from its 1910 inception, in a paper by Hermann Weyl, to its modernday extensions to the asymptotic analysis of nonlinear differential equations. The authors distill the classical theorems in the linear case and carefully map the progress from linear to nonlinear limitpoint results. The relationship between the limitpoint/limitcircle properties and the boundedness, oscillation, and convergence of solutions is explored, and in the final chapter, the connection between limitpoint/limitcircle problems and spectral theory is examined in detail. With over 120 references, many open problems, and illustrative examples, this work will be valuable to graduate students and researchers in differential equations, functional analysis, operator theory, and related fields.
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