Applied Mathematics and Mechanics

, Volume 22, Issue 4, pp 394–403

# Asymptotic Solutions of Boundary Value Problems for Third-Order Ordinary Differential Equations with Turning Points

• Fu-ru Jiang
• Qi-nian Jin
Article

## Abstract

Boundary value problems for third-order ordinary differential equations with turning points are studied as follows: $$\varepsilon y\prime \prime \prime + f\left( {x;\varepsilon } \right)y\prime \prime + g\left( {x;\varepsilon } \right)y\prime + h\left( {x;\varepsilon } \right)y = 0{\text{ }}\left( {{\text{ - }}a < x < b,0 < \varepsilon \ll 1} \right),$$, where f(x; 0) has several multiple zero points in (− a, b). The necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.

boundary value problems ordinary differential equations turning points asymptotic solutions

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