Exact solutions of iterative functional differential equations (Q817016)

The paper deals with nonlinear functional-differential equations of the form \(f(x_1,x_2,\dots, x_m\), \(y_1,y_2,\dots, y_n)= 0\), where \(f\) is a polynomial, \(x_i= x^{(i)}(p_iz)\), \(y_j= x^{[j]}(q_j z)\), \(x^{(i)}= d^ix/dz^i\), \(x^{(0)}= x\), \(x^{[j]}(z)= x(x^{[j-1]}(z))\), \(x^{[0]}(z)= z\) and \(p_i\), \(q_j\) are constants. Conditions are found for the existence of solutions of the form \(x=\lambda z^\mu\).