A generalization of a theorem of Reissig for a certain third order different equation

Abstract

In a previous paper [1] Reissig had established a boundedness result for an equation (1.1) in which f(x) is a bounded function. In the present paper that result of Reissig is extended to hold for an equation (1.4) in which the function ϑ is bounded and the coefficient ϕ, not necessarily constant, satisfies: $$\int\limits_0^x {\varphi \left( s \right)ds} - bx = 0\left( 1 \right) as \left| x \right| \to \infty $$ , for some constant b>0.