The higher-order Picone identity and comparison of half-linear differential equations of even order

作者：Jaros Jaroslav^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(18): 7513-7518.

DOI：10.1016/j.na.2011.08.006

• Half-linear differential operator
• Picone's identity

An identity of the Picone type for higher-order half-linear ordinary differential operators of the form l(alpha)[x] = Sigma(n)(j=0)(-1)(j)(p(j)phi(x((j))))((j)) and L-alpha[y] Sigma(n)(j=0)(-1)(j)(P-j phi(y((j))))((j)) where p(j) and P-j, j = 0, ... , n, are continuous functions defined on [a, b] and phi(u) := vertical bar u vertical bar(alpha) sgnu, alpha > 0, is derived and then the Sturmian comparison theory for the corresponding 2nth-order equations l(alpha)[x] = 0 and L-alpha[y] = 0 based on this identity is developed.

• 出版日期2011-12