A singular eigenvalue problem for second order linear ordinary differential equations.
Takaŝi, Kusano, Naito, Manabu (1997)
Memoirs on Differential Equations and Mathematical Physics
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Takaŝi, Kusano, Naito, Manabu (1997)
Memoirs on Differential Equations and Mathematical Physics
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A. Arena (1986/87)
Manuscripta mathematica
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Gunnar Aronsson (1984)
Manuscripta mathematica
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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.
Dmitry Golovaty (1997)
Manuscripta mathematica
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A. Dijksma, H.S.V. de Snoo (1973)
Manuscripta mathematica
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Zhou, W.S., Cai, S.F. (2006)
Lobachevskii Journal of Mathematics
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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.
Rabtsevich, V.A. (2000)
Memoirs on Differential Equations and Mathematical Physics
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