Singularly perturbed Dirichlet problems with subquadratic nonlinearities
Author:
Albert J. DeSanti
Journal:
Trans. Amer. Math. Soc. 303 (1987), 585-593
MSC:
Primary 35B25; Secondary 35J65
DOI:
https://doi.org/10.1090/S0002-9947-1987-0902786-4
MathSciNet review:
902786
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Abstract | References | Similar Articles | Additional Information
Abstract: Boundary and interior layer theory is provided for a class of singularly perturbed Dirichlet problems with subquadratic nonlinearities in the derivative terms. The results obtained generalize and extend well-known results on the semilinear problem.
- Herbert Amann, Existence and multiplicity theorems for semi-linear elliptic boundary value problems, Math. Z. 150 (1976), no. 3, 281–295. MR 430526, DOI https://doi.org/10.1007/BF01221152
- M. S. Berger and L. E. Fraenkel, On the asymptotic solution of a nonlinear Dirichlet problem, J. Math. Mech. 19 (1969/1970), 553–585. MR 0252813
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. II, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1989. Partial differential equations; Reprint of the 1962 original; A Wiley-Interscience Publication. MR 1013360
- Albert James DeSanti, Boundary and interior layer behavior of solutions of some singularly perturbed semilinear elliptic boundary value problems, J. Math. Pures Appl. (9) 65 (1986), no. 3, 227–262. MR 875158
- Albert J. DeSanti, Singularly perturbed quadratically nonlinear Dirichlet problems, Trans. Amer. Math. Soc. 298 (1986), no. 2, 733–746. MR 860390, DOI https://doi.org/10.1090/S0002-9947-1986-0860390-X
- Wiktor Eckhaus, Asymptotic analysis of singular perturbations, Studies in Mathematics and its Applications, vol. 9, North-Holland Publishing Co., Amsterdam-New York, 1979. MR 553107 P. C. Fife, Semilinear boundary value problems with small parameters, Arch. Rational Mech. Anal. 23 (1966/1967), 26-86.
- P. Faĭf and U. Grinli, Interior transition layers for elliptic boundary value problems with a small parameter, Uspehi Mat. Nauk 29 (1974), no. 4 (178), 103–130 (Russian). Translated from the English by L. P. Volevič; Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ, II. MR 0481510
- F. A. Howes, Singularly perturbed semilinear elliptic boundary value problems, Comm. Partial Differential Equations 4 (1979), no. 1, 1–39. MR 514718, DOI https://doi.org/10.1080/03605307908820090 ---, Some singularly perturbed nonlinear problems of elliptic type, Nonlinear Partial Differential Equations in Engineering and Applied Science, edited by R. L. Sternberg, A. J. Kalinowsky, and J. S. Papadakis, Dekker, New York, 1980, pp. 151-166.
- F. A. Howes, Perturbed elliptic problems with essential nonlinearities, Comm. Partial Differential Equations 8 (1983), no. 8, 847–874. MR 699312, DOI https://doi.org/10.1080/03605308308820288
- Walter G. Kelley, The Dirichlet problem for singularly perturbed quasilinear elliptic equations, J. Differential Equations 40 (1981), no. 1, 37–52. MR 614217, DOI https://doi.org/10.1016/0022-0396%2881%2990009-7
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Additional Information
Keywords:
Singular perturbation,
Dirichlet problems,
subquadratic nonlinearities,
differential inequalities
Article copyright:
© Copyright 1987
American Mathematical Society