Abstract
In this paper, by the technique and the method of diagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with:\(\varepsilon y'' = f(t,y,y',\varepsilon ), y(0,\varepsilon ) = a(\varepsilon ), y(1,\varepsilon ) = b(\varepsilon )\)
The existance of the solution and its asymptotic properties are discussed when the eigenvalues of Jacobi matrix fy′ has K negative real parts and N−K positive real parts.
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Communicated by Lin Zongchi
Supported by the Natural Science Foundation of Fujian Province
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Weizhang, H. Boundary value problem for a singularly perturbed nonlinear system. Appl Math Mech 18, 575–584 (1997). https://doi.org/10.1007/BF02454117
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DOI: https://doi.org/10.1007/BF02454117