Abstract
Consider the first-order linear difference equationwhere ๏ denotes the forward difference operator, i.e. ๐ฅ๐ฅ(๐) = ๐ฅ(๐ + 1) -๐ฅ(๐), {๐(๐)} โ is a nonnegative sequence of reals and k is a natural number.Sharp conditions for the oscillation of all solutions to this equation are presented when the well-known oscillation conditions