International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 821-824
doi:10.1155/S0161171290001156
Properties of solutions to a second order nonlinear differential equation
Allan J. Kroopnick
Office of Retirement and Survivors Insurance, Social Security Administration, 3-D-22 Operations Building, 6401 Security Boulevard, Baltimore, Maryland 21235, USA
Abstract
In this note, we show when all solutions to the nonlinear differential equation x″+c(t)f(x)g(x′)x′+a(t,x)=0 are bounded. Furthermore, the solutions are either oscillatory or monotonic and asymptotically stable.