An asymptotic theory for a class of nonlinear Robin problems. II
Author:
F. A. Howes
Journal:
Trans. Amer. Math. Soc. 260 (1980), 527552
MSC:
Primary 34E15
MathSciNet review:
574797
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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 righthand side grows faster than the square of the derivative.
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 E. A. Coddington and N. Levinson, A boundary value problem for a nonlinear differential equation with a small parameter, Proc. Amer. Math. Soc. 3 (1952), 7381. MR 0046517 (13:746h)
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 F. W. Dorr, S. V. Parter and L. F. Shampine, Applications of the maximum principle to singular perturbation problems, SIAM Rev. 15 (1973), 4388. MR 0320456 (47:8995)
 [3]
 L. E. El'sgol'c, Qualitative methods in mathematical analysis, Transl. Math. Mono., No. 12, Amer. Math. Soc., Providence, R. I., 1964. MR 0170048 (30:289)
 [4]
 A. Erdélyi, Singular perturbations of boundary value problems involving ordinary differential equations, SIAM J. Appl. Math. 11 (1963), 105116. MR 0152720 (27:2695)
 [5]
 S. Haber and N. Levinson, A boundary value problem for a singularly perturbed differential equation, Proc. Amer. Math. Soc. 6 (1955), 866872. MR 0074634 (17:618e)
 [6]
 W. Hahn, Stability of motion, Die Grundlehren der mathematischen Wissenschaften, SpringerVerlag, New York, 1967. MR 0223668 (36:6716)
 [7]
 J. W. Heidel, A secondorder nonlinear boundary value problem, J. Math. Anal. Appl. 48 (1974), 493503. MR 0377163 (51:13336)
 [8]
 F. A. Howes, An asymptotic theory for a class of nonlinear Robin problems, J. Differential Equations 30 (1978), 192234. MR 513270 (80a:34080)
 [9]
 , Singularly perturbed superquadratic boundary value problems, J. Nonlinear Analysis 3 (1979), 175192. MR 525970 (80f:34017)
 [10]
 E. L. Ince, Ordinary differential equations, Dover, New York, 1956. MR 0010757 (6:65f)
 [11]
 L. K. Jackson, Subfunctions and secondorder ordinary differential inequalities, Advances in Math. 2 (1968), 307363. MR 0229896 (37:5462)
 [12]
 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), 125143. MR 0223638 (36:6686)
 [13]
 R. E. O'Malley, Jr., On singular perturbation problems with interior nonuniformities, J. Math. Mech. 19 (1970), 11031112.
 [14]
 L. M. Perko, Boundary layer analysis of the wide capillary tube, Arch. Rational Mech. Anal. 45 (1972), 120133. MR 0345511 (49:10247)
 [15]
 , Singularly perturbed twopoint boundary value problems with , nonlinearities, Arch. Rational Mech. Anal. (to appear).
 [16]
 M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, PrenticeHall, Englewood Cliffs, N. J., 1967. MR 0219861 (36:2935)
 [17]
 A. B. Vasil'eva, Asymptotic behavior of solutions to certain problems involving nonlinear differential equations containing a small parameter multiplying the highest derivatives, Russian Math. Surveys 18 (1963), 1384. MR 0158137 (28:1363)
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DOI:
http://dx.doi.org/10.1090/S00029947198005747976
PII:
S 00029947(1980)05747976
Article copyright:
© Copyright 1980
American Mathematical Society
