The Existence Of Non-extreme Solution Of One Type Third-order Non-linear Differential Equation

This paper is concerned -with non-extreme positive-solutions of the third-order nonlinear differential equationwhereα> 0,β> 0, p(t) and q(t) are continuous functions on an infinite interval [a,∞) satisfying p(t) > 0 and q(t) > 0, (t > a). Under the assumptionsα>βandα=β,sufficient integral conditions are established for the existence of type (I) solutions and under the assumptionsα<β, necessary and sufficient integral conditions are established for the existence of non-extreme positive solutions.