GLOBAL STABLE AND UNSTABLE MANIFOLDS FOR A CLASS OF SEMILINEAR EQUATIONS WITH SECTORIALLY DICHOTOMOUS OPERATOR

Lianwang Deng; Dongmei Xiao

doi:10.11948/2019.373

2019 Volume 9 Issue 1

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Lianwang Deng, Dongmei Xiao. GLOBAL STABLE AND UNSTABLE MANIFOLDS FOR A CLASS OF SEMILINEAR EQUATIONS WITH SECTORIALLY DICHOTOMOUS OPERATOR[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 373-399. doi: 10.11948/2019.373

Citation:

Lianwang Deng, Dongmei Xiao. GLOBAL STABLE AND UNSTABLE MANIFOLDS FOR A CLASS OF SEMILINEAR EQUATIONS WITH SECTORIALLY DICHOTOMOUS OPERATOR[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 373-399. doi: 10.11948/2019.373

GLOBAL STABLE AND UNSTABLE MANIFOLDS FOR A CLASS OF SEMILINEAR EQUATIONS WITH SECTORIALLY DICHOTOMOUS OPERATOR

Lianwang Deng^1, ,,
Dongmei Xiao¹

1.
School of Mathematical Sciences, Shanghai Jiao Tong University, Dongchuan RD, Shanghai, 200240, China

Corresponding author: Email address:denglianwang@sjtu.edu.cn.(L. Deng)

Abstract

Abstract

In this paper, the existence and smoothness of global stable and unstable manifolds at an equilibrium are established for a class of semilinear equations with sectorially dichotomous operator. As an application, an elliptic PDE in infinite cylindrical domain is discussed.
- Semilinear equations /
- sectorially dichotomous operator /
- dichotomous solution /
- stable and unstable manifolds
MSC: 47D06, 37D10, 34D09

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References

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