Electron. J. Diff. Equ., Vol. 2011 (2011), No. 80, pp. 1-5.

Hyers-Ulam stability for second-order linear differential equations with boundary conditions

Pasc Gavruta, Soon-Mo Jung, Yongjin Li

Abstract:
We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ \beta (x) y = 0$ with $y(a) = y(b) =0$, then there exists an exact solution of the differential equation, near y.

Submitted April 26, 2011. Published June 20, 2011.
Math Subject Classifications: 34K20, 26D10.
Key Words: Hyers-Ulam stability, differential equation.

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Pasc Gavruta
Department of Mathematics, University Politehnica of Timisoara
Piata Victoriei, No. 2, 300006 Timisoara, Romania
email: pgavruta@yahoo.com
Soon-Mo Jung
Mathematics Section, College of Science and Technology
Hongik University, 339-701 Jochiwon, Korea
email: smjung@hongik.ac.kr
Yongjin Li
Department of Mathematics, Sun Yat-Sen University
Guangzhou 510275, China
email: stslyj@mail.sysu.edu.cn

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