Electron. J. Diff. Eqns., Vol. 2004(2004), No. 85, pp. 1-20.

Asymptotic stability for second-order differential equations with complex coefficients

Gro R. Hovhannisyan

We prove asymptotical stability and instability results for a general second-order differential equations with complex-valued functions as coefficients. To prove asymptotic stability of linear second-order differential equations, we use the technique of asymptotic representations of solutions and error estimates. For nonlinear second-order differential equations, we extend the asymptotic stability theorem of Pucci and Serrin to the case of complex-valued coefficients.

Submitted April 19, 2004. Published June 13, 2004.
Math Subject Classifications: 34D20, 34E05.
Key Words: Asymptotic stability; asymptotic representation; WKB solution; second order differential equation.

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Gro R. Hovhannisyan
Kent State University, Stark Campus
6000 Frank Ave. NW
Canton, OH 44720-7599, USA
email: ghovhannisyan@stark.kent.edu

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