Differential and Integral Equations

Nonlinear perturbations of some non-invertible differential operators

Alessandro Fonda and Rodica Toader

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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

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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

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