Nonlinear limit-point type solutions of nth order differential equations

[摘要] We continue the study of limit-point/limit-circle type differential equations of the nth order. In particular, we show that the differential expression y((4k)) + ry, k = 1, 2,..., is never of the limit-circle type as long as r is not an unbounded oscillatory function; this partially answers an open question and generalizes out result for n = 4. This follows as a consequence of new results on the nonlinear limit-point/limit-circle problem for the equation y(n) = r(t)f(y, y',...,y(n - 1)). (C) 1997 Academic Press.

[发布日期] 1997-05-01