On Asymptotic Equivalence for Nonlinear ODE with Applications

Vojislav Marić Serbian Academy of Sci. and Arts Beograd, Serbia - Montenegro

Let m be a real number, p, q, Q continuous functions on [a, ∞), a > 0 and p(t) positive.

The existence and asymptotics for t → ∞ of some solutions of the equation (p(t)x′)′ + q(t)x = Q(t)|x|^{m}sgnx is obtained via the Schauder - Tychonoff fixed point theorem and using a fundamental set of solutions of the associate linear equation which is supposed to be nonoscillatory.

Application to some equations of mathematical physics (biophysics in particular) is presented.