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Vrábeľ, Róbert
Upper and lower solutions for singularly perturbed semilinear Neumann's problem. (English). Mathematica Bohemica, vol. 122 (1997), issue 2, pp. 175-180
MSC: 34B15, 34E15, 34E20, 35B10 | MR 1460947 | Zbl 0893.34052 | DOI: 10.21136/MB.1997.125912
Keywords:
singularly perturbed equation; Neumann’s problem
Summary:
The paper establishes sufficient conditions for the existence of solutions of Neumann's problem for the differential equation $\mu y"+ky=f(t,y)$ which tend to the solution of the reduced problem $ky=f(t,y)$ on $[0,1]$ as $\mu\to0.$
References:
[1] R. E. O'Malley, Jr.: Phase-plane solutions to some singular perturbation problems. J. Math. Anal. Appl. 54, (1976), 449-466. DOI 10.1016/0022-247X(76)90214-6 | MR 0450722 | Zbl 0334.34050
[2] J. Mawhin: Points fixes, points critiques ct problemes aux limites. Sémin. Math. Sup. no. 92, Presses Univ. Montгéal, Montréal, 1985. MR 0789982
[3] K. W. Chang F. A. Howes: Nonlinear singular perturbation phenomena. Springer-Verlag, 1984. MR 0764395
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