Existence and convergence of solutions to singular boundary value problems for second-order ordinary differential equations and applications. (English) Zbl 1031.34053
Summary: The authors consider singular boundary value problems for second-order quasilinear ordinary differential equations and prove existence and convergence on second-order perturbation terms. The result is applied to solve the Riemann problem for \(2\times 2\) hyperbolic conservation laws.
MSC:
| 34E15 | Singular perturbations for ordinary differential equations |
| 35L65 | Hyperbolic conservation laws |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
References:
| [1] | DOI: 10.1007/BF00249087 · Zbl 0262.35034 · doi:10.1007/BF00249087 |
| [2] | Deng, Zongqi. 1987. ”Boundary Value Problems On Ordinary Differential Equations And Sturmian Comparison Theory”. Hubei: Central China Normal University Press. |
| [3] | DOI: 10.1016/0022-0396(83)90027-X · Zbl 0521.35035 · doi:10.1016/0022-0396(83)90027-X |
| [4] | Zhu C.J., Proc.Roy.Soc 126 pp 719– (1996) |
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