Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A singular perturbation method. Part II


Author: N. D. Fowkes
Journal: Quart. Appl. Math. 26 (1968), 71-85
DOI: https://doi.org/10.1090/qam/99865
MathSciNet review: QAM99865
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Abstract: This paper extends the work of Part I to the partial differential equation

$\displaystyle {\epsilon ^3}{\nabla ^2}\psi - g\left( x \right)\psi = 0$

where $ \epsilon $ is a small positive parameter and $ g\left( x \right)$ is a bounded function of $ x$ which vanishes along simple closed surfaces in the solution domain. In particular, the eigenproblem corresponding to the case in which $ g\left( x \right)$ is positive at infinity and in which the boundary condition $ \psi \to 0$ as $ \left\vert x \right\vert \to \infty $ is imposed, is considered. One class of eigensolutions is extracted.

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DOI: https://doi.org/10.1090/qam/99865
Article copyright: © Copyright 1968 American Mathematical Society

American Mathematical Society