On Singular Perturbation Method of Perturbed Bifurcation Problems

Chu Zheng-you; Cheng Chang-jun

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1984 > 5(4): 527-534

Chu Zheng-you, Cheng Chang-jun. On Singular Perturbation Method of Perturbed Bifurcation Problems[J]. Applied Mathematics and Mechanics, 1984, 5(4): 527-534.

Citation:

Chu Zheng-you, Cheng Chang-jun. On Singular Perturbation Method of Perturbed Bifurcation Problems[J]. Applied Mathematics and Mechanics, 1984, 5(4): 527-534.

Citation:

Chu Zheng-you, Cheng Chang-jun. On Singular Perturbation Method of Perturbed Bifurcation Problems[J]. Applied Mathematics and Mechanics, 1984, 5(4): 527-534.

PDF( 483 KB)

On Singular Perturbation Method of Perturbed Bifurcation Problems

Lanzhou University, Lanzhou

Received Date: 1983-08-15
Publish Date: 1984-08-15

Abstract

Abstract

In this paper, the general mathematical principle is over-all explained and a new general technique is presented in order to calculate uniformly asymptotic expansions of solutions of the perturbed bifurcation problem (1.6) in the vicinity of y=0, λ=0,δ=0, by means of singular perturbation method. Simultaneously, Newton's polygon^[4] is generalized. Finally, the calculating results of two examples are given.

FullText(HTML)

References(5)

References

[1]	Sather, D.,Branching of solutions of an equation in Hilbert space, Arch. Rat. Mech. Anal, 36,(1970), 47-64.
[2]	Temme, N. M.(ed.), Nonlinear Analysis, vol. 2, Amsterdam,(1976).
[3]	Matkowsky, B. J., and R. L. Reiss, Singularperturbation of bifurcations, SIAM J. Appl. Math. Vol. 33, No. 2,(1977), 230-255.
[4]	Vainberg, M. M., and V. A. Trenogin, Theory of Branching of Solutions of Nonlinear Equations,(1974).
[5]	Timoshenko, S. P., and J. M. Gere, Theory of Elastic Stability, McGraw-Hill, New York,(1961).