A nonresonance result for strongly nonlinear second order {ODE}'s

Abstract

A {\em nonresonance result} is obtained for the Dirichlet boundary value problem $$ (P)\qquad\begin{cases}-(\phi(u'))'=f(u)+e(t), \quad t\in(0,T),\ T>0, \\ u(0)=u(T)=0, \end{cases} $$ where $\phi$ is an odd, increasing homeomorphism from $\mathbb R$ onto $\mathbb R$, $f:\mathbb R \to \mathbb R$ is a continuous function satisfying some resonance condition and $e \in L^\infty [0,T]$. This result is obtained by using a time-map approach and topological degree.