| Title:
|
On singular perturbation of nonlinear two-point boundary value problems (English) |
| Author:
|
Baxley, John V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
27 |
| Issue:
|
3 |
| Year:
|
1977 |
| Pages:
|
363-377 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34E15 |
| idZBL:
|
Zbl 0376.34009 |
| idMR:
|
MR0437867 |
| DOI:
|
10.21136/CMJ.1977.101474 |
| . |
| Date available:
|
2008-06-09T14:24:00Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101474 |
| . |
| Reference:
|
[1] E. A. Coddington, N. Levinson: A boundary value problem for a nonlinear differential equation with a small parameter.Proc. Amer. Math. Soc. 3 (1952), pp. 73-81. Zbl 0046.09503, MR 0046517, 10.1090/S0002-9939-1952-0046517-3 |
| Reference:
|
[2] J. W. Bebernes, Robert Gaines: Dependence on boundary data and a generalized boundary-value problem.J. Differential Equations 4 (1968), pp. 359-368. MR 0228738, 10.1016/0022-0396(68)90022-3 |
| Reference:
|
[3] J. W. Bebernes, Robert Gaines: A generalized two-point boundary value problem.Proc. Amer. Math. Soc. 19 (1968), pp. 749-754. MR 0226098, 10.1090/S0002-9939-1968-0226098-3 |
| Reference:
|
[4] F. X. Dorr S. V. Parter, L. F. Shempine: Applications of the maximum principle to singular perturbation problems.Siam Review 15 (1973), pp. 43 - 88. MR 0320456, 10.1137/1015002 |
| Reference:
|
[5] W. Eckhaus, E. M. DeJager: Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type.Arch. Rational Mech. Anal. 23 (1966) pp. 26-86. MR 0206464, 10.1007/BF00281135 |
| Reference:
|
[6] A. Erdelyi: Approximate solutions of a nonlinear boundary value problem.Arch. Rational Mech. Anal. 29 (1968), pp. 1-17. Zbl 0155.13203, MR 0231002, 10.1007/BF00256455 |
| Reference:
|
[7] A. Erdelyi: On a nonlinear boundary value problem involving a small parameter.J. Australian Math. Soc. 2 (1962), pp. 425-439. Zbl 0161.06201, MR 0145162, 10.1017/S1446788700027440 |
| Reference:
|
[8] A. Erdelyi: The integral equations of asymptotic theory, in Asymptotic Solutions of Differential Equations and Their Applications.Wiley, New York, 1964, pp. 211 - 229. MR 0170061 |
| Reference:
|
[9] Gerald Houghton: Approximation methods to evaluate the effect of axial dispersion in isothermal flow reactors.Can. J. Chem. Engng. 40 (1962), pp. 188-193. 10.1002/cjce.5450400503 |
| Reference:
|
[10] H. B. Keller: Existence theory for two point boundary value problems.Bull. Amer. Math. Soc. 72 (1966), pp. 729-731. Zbl 0146.11503, MR 0192116, 10.1090/S0002-9904-1966-11572-0 |
| Reference:
|
[11] H. O. Kreiss, S. V. Parter: Remarks on singular perturbations with turning points.SIAM J. Math. Anal. 5 (1974), pp. 230-251. Zbl 0302.34074, MR 0348212, 10.1137/0505025 |
| Reference:
|
[12] R. E. O'Malley, Jr.: Topics in singular perturbations.Advances in Math. 2 (1968), pp. 365-470. Zbl 0203.40101, MR 0232056, 10.1016/0001-8708(68)90023-6 |
| Reference:
|
[13] R. E. О'Маllеуу, Jr.: A boundary value problem for certain non-linear second order differential equations with a small parameter.Arch. Rational Mech. Anal. 29 (1968), pp. 66- 74. MR 0231003, 10.1007/BF00256459 |
| Reference:
|
[14] R. E. O'Malley, Jr.: A non-linear singular perturbation problem arising in the study of chemical flow reactors.J. Inst. Maths. Applies. 6 (1969), pp. 12-20. 10.1093/imamat/6.1.12 |
| Reference:
|
[15] S. V. Parter: Singular perturbations of second order differential equations.(unpublished paper). |
| Reference:
|
[16] S. V. Parter: Remarks on singular perturbation of certain non-linear two-point boundary value problems.SIAM J. Math, Anal. 3 (1972), pp. 295-299. MR 0312006, 10.1137/0503029 |
| Reference:
|
[17] S. V. Parter: Remarks on the existence theory for multiple solutions of a singular perturbation problem.SIAM J. Math. Anal. 3 (1972), pp. 496-505. Zbl 0251.34037, MR 0318620, 10.1137/0503047 |
| Reference:
|
[18] M. H. Protter, H. F. Weinberger: Maximum Principles in Differential Equations.Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 0219861 |
| . |
