Necessary and Sufficient Conditions for Oscillation of Second-Order Delay Differential Equations

Abstract

Abstract In this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form ( r ( x ′ ) γ ) ′ ( t ) + q ( t ) x α ( τ ( t ) ) = 0 {\left( {r{{\left( {x'} \right)}^\gamma }} \right)^\prime }\left( t \right) + q\left( t \right){x^\alpha }\left( {\tau \left( t \right)} \right) = 0 Under the assumption ∫∞(r(n))−1/γdη=∞, we consider the two cases when γ > α and γ < α. Further, some illustrative examples showing applicability of the new results are included, and state an open problem.