On Boundedness of a Certain Non-Linear Differential Equation of Third Order

Abstract

This paper presents sufficient conditions for all solutions as well as their derivatives up to second order to x"' + a(t)f(x')x '' + b(t, x, x') +c(t)g(x) = et, x, x', x '') to be bounded. What is more, it shows that all the solutions are in L-p[0,infinity) Under somewhat more restrictive conditions.