First posed by Hermann Weyl in 1910, the limita "point/limita
"circle problem has inspired, over the last century, several new
developments in the asymptotic analysis of nonlinear differential
equations. This monograph traces the evolution of this problem from
its inception to its modern-day extensions to the study of
deficiency indices and analogous properties for nonlinear
equations.
The book opens with a discussion of the problem in the linear
case, as 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
limita "point results. The relationship between the limita
"point/limita "circle properties and the boundedness, oscillation,
and convergence of solutions is explored, and in the final chapter,
the connection between limita "point/limita "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,
operator theory, and related fields.
General
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