On some nonlinear ordinary differential equations with advanced arguments Original Research Article

The paper deals with ODEs with an advanced argument, in particular, with such equations as y′(t)=(y(βt))1/β, the simplest example is View the MathML source. The corresponding initial-value problem with y(0)=y0>0 has three types of solutions: (a) a unique analytic solution, (b) solutions of subexponential growth, and (c) for every λ>0 a solution that behaves like eλt as t→∞. In the case y0=0 there is (besides y≡0) a positive solution, for some β>1 it can be analytic, but the above example β=2 admits infinitely many analytic solutions.