## Differential and Integral Equations

### Nonlinear perturbations of some non-invertible differential operators

#### Abstract

We consider perturbations, depending on a small parameter $\lambda$, of a non-invertible differential operator having a nonnegative spectrum. Given a pair of lower and upper solutions, belonging to the kernel of the differential operator, without any prescribed order, we prove the existence of a solution, when $\lambda$ is sufficiently small. Our method of proof has the advantage of permitting a uniform choice of $\lambda$ for a whole class of functions. Applications are given in a variety of situations, ranging from ODE problems to equations of parabolic type, or involving the $p\,$-Laplacian operator.

#### Article information

Source
Differential Integral Equations, Volume 22, Number 9/10 (2009), 949-978.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019517

Mathematical Reviews number (MathSciNet)
MR2553065

Zentralblatt MATH identifier
1240.34073

#### Citation

Fonda, Alessandro; Toader, Rodica. Nonlinear perturbations of some non-invertible differential operators. Differential Integral Equations 22 (2009), no. 9/10, 949--978. https://projecteuclid.org/euclid.die/1356019517