An asymptotic theory for a class of nonlinear Robin problems. II
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- by F. A. Howes
- Trans. Amer. Math. Soc. 260 (1980), 527-552
- DOI: https://doi.org/10.1090/S0002-9947-1980-0574797-6
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Abstract:
Various asymptotic phenomena exhibited by solutions of singularly perturbed Robin boundary value problems are studied in the case when the right-hand side grows faster than the square of the derivative.References
- Earl A. Coddington and Norman Levinson, A boundary value problem for a nonlinear differential equation with a small parameter, Proc. Amer. Math. Soc. 3 (1952), 73–81. MR 46517, DOI 10.1090/S0002-9939-1952-0046517-3
- F. W. Dorr, S. V. Parter, and L. F. Shampine, Applications of the maximum principle to singular perturbation problems, SIAM Rev. 15 (1973), 43–88. MR 320456, DOI 10.1137/1015002
- L. È. Èl′sgol′c, Qualitative methods in mathematical analysis, Translations of Mathematical Monographs, Vol. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170048
- A. Erdélyi, Singular perturbations of boundary value problems involving ordinary differential equations, J. Soc. Indust. Appl. Math. 11 (1963), 105–116. MR 152720
- S. Haber and N. Levinson, A boundary value problem for a singularly perturbed differential equation, Proc. Amer. Math. Soc. 6 (1955), 866–872. MR 74634, DOI 10.1090/S0002-9939-1955-0074634-3
- Wolfgang Hahn, Stability of motion, Die Grundlehren der mathematischen Wissenschaften, Band 138, Springer-Verlag New York, Inc., New York, 1967. Translated from the German manuscript by Arne P. Baartz. MR 0223668
- J. W. Heidel, A second-order nonlinear boundary value problem, J. Math. Anal. Appl. 48 (1974), 493–503. MR 377163, DOI 10.1016/0022-247X(74)90172-3
- F. A. Howes, An asymptotic theory for a class of nonlinear Robin problems, J. Differential Equations 30 (1978), no. 2, 192–234. MR 513270, DOI 10.1016/0022-0396(78)90014-1
- F. A. Howes, Singularly perturbed superquadratic boundary value problems, Nonlinear Anal. 3 (1979), no. 2, 175–192. MR 525970, DOI 10.1016/0362-546X(79)90075-0
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
- Lloyd K. Jackson, Subfunctions and second-order ordinary differential inequalities, Advances in Math. 2 (1968), 307–363. MR 229896, DOI 10.1016/0001-8708(68)90022-4
- W. E. Johnson and L. M. Perko, Interior and exterior boundary value problems from the theory of the capillary tube, Arch. Rational Mech. Anal. 29 (1968), 125–143. MR 223638, DOI 10.1007/BF00281362 R. E. O’Malley, Jr., On singular perturbation problems with interior nonuniformities, J. Math. Mech. 19 (1970), 1103-1112.
- L. M. Perko, Boundary layer analysis of the wide capillary tube, Arch. Rational Mech. Anal. 45 (1972), 120–133. MR 345511, DOI 10.1007/BF00253041 —, Singularly perturbed two-point boundary value problems with ${(y’)^n},\,n\, > \,2$, nonlinearities, Arch. Rational Mech. Anal. (to appear).
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- A. B. Vasil′eva, Asymptotic behaviour of solutions of certain problems for ordinary non-linear differential equations with a small parameter multiplying the highest derivatives, Uspehi Mat. Nauk 18 (1963), no. 3 (111), 15–86 (Russian). MR 0158137
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 260 (1980), 527-552
- MSC: Primary 34E15
- DOI: https://doi.org/10.1090/S0002-9947-1980-0574797-6
- MathSciNet review: 574797