Differential and Integral Equations

Nonlinear perturbations of some non-invertible differential operators

Alessandro Fonda and Rodica Toader

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly- Laplacian
Secondary: 34A40: Differential inequalities [See also 26D20] 34B08: Parameter dependent boundary value problems 34B20: Weyl theory and its generalizations 34B34 35K59: Quasilinear parabolic equations


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

Export citation