Abstract :
In the article we consider the resonant Dirichlet problem,
u Žt . uŽt . g Žu Žt .. f Žt ., t 0, ,
Ž1.
uŽ0. uŽ . 0,
where g is a continuous function having finite limits at plus and minus infinity:
gŽ . gŽ .. Imposing gŽ . gŽ s. gŽ . for any s we formulate a
necessary condition. Our main result provides a characteristic of the set of
functions f C 0, T , such that Ž1. has a solution. However, to prove this we need
that g is odd, increasing, and satisfies a certain asymptotic condition at infinity, in
addition. The main tools used are Lyapunov Schmidt reduction and certain
asymptotical methods.
