Displaying similar documents to “Stability Theorems for Singular Perturbation of Eigenvalues.”

Positive solutions and eigenvalue intervals of a singular third-order boundary value problem

Qingliu Yao (2011)

Annales Polonici Mathematici

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This paper studies positive solutions and eigenvalue intervals of a nonlinear third-order two-point boundary value problem. The nonlinear term is allowed to be singular with respect to both the time and space variables. By constructing a proper cone and applying the Guo-Krasnosel'skii fixed point theorem, the eigenvalue intervals for which there exist one, two, three or infinitely many positive solutions are obtained.

On Threshold Eigenvalues and Resonances for the Linearized NLS Equation

V. Vougalter (2010)

Mathematical Modelling of Natural Phenomena

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We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.