Oscillation Conditions for a Third-Order Linear Equation.

Abstract

Consider the equation (1.1) u+p(t)u=0 were p is a locally integrable function. A solution of Eq. is defined as a function u locally absolutely continuous together with its first-and second-order derivatives and satisfying the equation almost everywhere. A nontrivial solution of Eq.(1.1)is said to be oscillating if it has infini tely many zeros and nonoscillating otherwise. Equation (1.1) is oscillating if it has at least one oscillating solution and nonoscillating otherwise. In the present paper, we prove integral oscillation criteria for Eq. (1.1), we assume that p is of constant sign.