Advances in Differential Equations

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

Mabel Cuesta and Marta García-Huidobro

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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.


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