Publication details

The nonlinear limit-point/limit-circle problem


BARTUŠEK Miroslav DOŠLÁ Zuzana GRAEF John R.

Year of publication 2006
Type Monograph
MU Faculty or unit

Faculty of Science

Description First posed by H.Weyl in 1910, the limit-point/limit-circle problem has inspired, over the last century, several new developments in the asymptotic analysis of nonlinear differential equations. The book opens with a discussion of the problem in the linear case, as H.Weyl originally stated it, and then proceeds to a generalization for nonlinear higher order equations. En route, the authors distill the classical theorems for second and higher-order linear equations, and carefully map the progression to nonlinear limit-point results. The relationship between the limit-point/limit-circle properties and the boundedness, oscillation, and convergence of solutions is explored, and the connection between limit-point/limit-circle 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, and related fields
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