On the principal eigenvalue in a singular perturbation problem with hyperbolic limit points and circles

DOI10.1016/0022-0396(80)90092-3zbMath0413.35010OpenAlexW2022197962MaRDI QIDQ1260525

Yuri Kifer

Publication date: 1980

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(80)90092-3

zbMATH Keywords

fixed pointsDirichlet problemeigenvaluesdynamical systemdiffusion processsingular perturbation problemhyperbolic dynamical systemasymptotic behavior of the principal eigenvalueprobabilistic techniquesecond order nondegenerate elliptic differential operator

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Fixed-point theorems (47H10) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

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Cites Work

• Unnamed Item
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• The fundamental solution of a linear parabolic equation containing a small parameter
• Hyperbolicity and chain recurrence
• Stability theorems and hyperbolicity in dynamical systems
• ON SMALL RANDOM PERTURBATIONS OF SOME SMOOTH DYNAMICAL SYSTEMS
• On the Asymptotic Behavior of the First Eigenvalue of a Second-Order Differential Operator with Small Parameter in Higher Derivatives
• On the Asymptotics of the Transition Density of Processes with Small Diffusion

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