Power Function Solutions of Iterative Functional Differential Equations with Some Conditions

Abstract

Iterative functional differential equations occur in many problems of physics and other sciences. This article is concerned with three equations x⁽ⁿ⁾ (z) = Az^j ( x^[m] (z) )^k, x⁽ⁿ⁾ (z) = A ( x^[m_i] (q_iz) )^k_i  and a more general equation ( x^(n_i) (p_iz) )^N_i = Az^j  ( x^[m_i] (q_iz) )^M_i .
We consider the existence of power solutions of the form x(z) = z for those three equations with given conditions.