Multiple Nonnegative Solutions for a Class IVPs for Second Order ODEs

Abstract

We study  a class of initial   value problems  for second order ODEs. The interesting points of our
results are that the nonlinearity depends on the solution and its derivative and may change sign. Moreover, it satisfies general
polynomial growth conditions. A new topological approach is applied to prove the existence of at least two  nonnegative classical solutions.  The arguments are based upon   a recent  theoretical result.