## Advances in Differential Equations

- Adv. Differential Equations
- Volume 6, Number 10 (2001), 1219-1254.

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

Mabel Cuesta and Marta García-Huidobro

#### 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.

#### Article information

**Source**

Adv. Differential Equations, Volume 6, Number 10 (2001), 1219-1254.

**Dates**

First available in Project Euclid: 2 January 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1357140393

**Mathematical Reviews number (MathSciNet)**

MR1850388

**Zentralblatt MATH identifier**

1023.34014

**Subjects**

Primary: 34B15: Nonlinear boundary value problems

Secondary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]

#### Citation

Cuesta, Mabel; García-Huidobro, Marta. A nonresonance result for strongly nonlinear second order {ODE}'s. Adv. Differential Equations 6 (2001), no. 10, 1219--1254. https://projecteuclid.org/euclid.ade/1357140393