Title: <i>A Priori</i> Estimates for Solutions of Singular Perturbations with a Turning Point
Abstract:A priori estimates are derived for the solutions of the boundary value problem εy″ + a ( x ) y′ + b ( x ) y = f ( x ), c ⩽ x ⩽ d , y ( c ) = α , y ( d ) = β . Here 0 < ε ≪ 1 is a small parameter an...A priori estimates are derived for the solutions of the boundary value problem εy″ + a ( x ) y′ + b ( x ) y = f ( x ), c ⩽ x ⩽ d , y ( c ) = α , y ( d ) = β . Here 0 < ε ≪ 1 is a small parameter and a ( x ) has a single simple zero in [ c,d ] (the turning point). It is shown that the solutions of this problem are uniformly bounded for ε →0 by the norms of f , α and β if and only if b ( x )<0 at the turning point. However, in certain cases there are weak a priori estimates for the solutions even if this condition is not fulfilled.Read More
Publication Year: 1977
Publication Date: 1977-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 36
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