Existence and stability of transition layers
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- Hale, J.K. & Sakamoto, K. Japan J. Appl. Math. (1988) 5: 367. doi:10.1007/BF03167908
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For a second order nonautonomous singularly perturbed ordinary differential equation with Neumann boundary conditions, the existence of single transition layer solutions is proved by using the method of Liapunov-Schmidt. The method also gives the stability of these solutions as an equilibrium point of a parabolic equation.