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September/October 2009 Nonlinear perturbations of some non-invertible differential operators
Alessandro Fonda, Rodica Toader
Differential Integral Equations 22(9/10): 949-978 (September/October 2009). DOI: 10.57262/die/1356019517


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.


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Alessandro Fonda. Rodica Toader. "Nonlinear perturbations of some non-invertible differential operators." Differential Integral Equations 22 (9/10) 949 - 978, September/October 2009.


Published: September/October 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.34073
MathSciNet: MR2553065
Digital Object Identifier: 10.57262/die/1356019517

Primary: 35J91
Secondary: 34A40 , 34B08 , 34B20 , 34B34 , 35K59

Rights: Copyright © 2009 Khayyam Publishing, Inc.

Vol.22 • No. 9/10 • September/October 2009
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