Existence and convergence of solutions of singular boundary value problems for second order ordinary differential equations and applications

Abstract

In this paper,we consider the 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 2×2 hyperbolic conservation laws,which is a partial differential equation arising in applied mathematical area.

Keywords:

• Riemann problem
• singular boundary value problems
• second order quasilinear ordinary differential equations
• hyperbolic conservation laws

AMS:

• 34B15
• 34E15
• 35L65