Continuability,boundness and asymptotic behavior of solutions ofx″ +q(t)f(x)=r(t)

Summary In addition to obtaining sufficient conditions for continuability of solutions of x″ + q(t)f(x)=r(t), some sufficient conditions and some necessary and sufficient conditions for boundedness are obtained. The asymptotic behavior of solutions is studied through examination of r(t)/q(t) as t → ∞. Supported by Mississippi State University Biological and Physical Sciences Research Institute. Entrata in Redazione il 6 febbraio 1973.