Oscillation of solutions to fourth-order trinomial delay differential equations

Abstract

The objective of this article is to study the oscillation properties of the solutions to the fourth-order linear trinomial delay differential equation $$ y^{(4)}(t)+p(t)y'(t)+q(t)y(\tau(t))=0. $$ Applying suitable comparison principles, we present new criteria for oscillation. In contrast with the existing results, we establish oscillation of all solutions, and essentially simplify the examination process for oscillation. An example is included to illustrate the importance of results obtained.

Keywords

• Fourth-order functional differential equation
• oscillation
• delay argument
• comparison theorem