Instability of solutions for certain nonlinear vector differential equations of fourth order

The main purpose of this paper is to give a result with explanatory example that deals directly with the instability of the trivial solution of a certain nonlinear vector differential equation of the fourth order. The result established here improves and includes a well-known instability result established for a scalar nonlinear differential equation of the fourth order. Published in Neliniini Kolyvannya, Vol. 12, No. 1, pp. 120–129, January–March, 2009.