scholarly journals A Study of Periodic Solution of a Duffing’s Equation Using Implicit Function Theorem

2018 ◽  
Vol 08 (10) ◽  
pp. 459-464
Author(s):  
E. O. Eze ◽  
J. N. Ezeora ◽  
U. E. Obasi
Keyword(s):  
Periodic Solution ◽  
Implicit Function Theorem ◽  
Implicit Function ◽  
Duffing's Equation ◽  
Duffing’S Equation

scholarly journals Boundedness and convergence of solutions of Duffing’s equation

1977 ◽  
Vol 66 ◽  
pp. 151-166 ◽  
Author(s):  
Kenichi Shiraiwa
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Periodic Function ◽  
Positive Constant ◽  
Boundedness Of Solutions ◽  
Duffing's Equation ◽  
Convergence Of Solutions ◽  
Duffing’S Equation

In this paper, we shall discuss boundedness of solutions of the equationunder suitable conditions. And we shall discuss asymptotic stability of a periodic solution and convergence of solutions for the equationfor a positive constant cand a periodic function e(t)under some restricted conditions.

The Origin and Bifurcation of Disclinations in the Gauge Field Theory of Dislocation and Disclination Continuum

1998 ◽  
Vol 12 (25) ◽  
pp. 2599-2617 ◽  
Author(s):  
Guo-Hong Yang ◽  
Yishi Duan
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Implicit Function Theorem ◽  
Taylor Expansion ◽  
Gauge Field Theory ◽  
Implicit Function ◽  
Quantum Numbers ◽  
Topological Quantum ◽  
Topological Current ◽  
Limit Points

In the 4-dimensional gauge field theory of dislocation and disclination continuum, the topological current structure and the topological quantization of disclinations are approached. Using the implicit function theorem and Taylor expansion, the origin and bifurcation theories of disclinations are detailed in the neighborhoods of limit points and bifurcation points, respectively. The branch solutions at the limit points and the different directions of all branch curves at 1-order and 2-order degenerated points are calculated. It is pointed out that an original disclination point can split into four disclinations at one time at most. Since the disclination current is identically conserved, the total topological quantum numbers of these branched disclinations will remain constant during their origin and bifurcation processes. Furthermore, one can see the fact that the origin and bifurcation of disclinations are not gradual changes but sudden changes. As some applications of the proposal theory, two examples are presented in the paper.

scholarly journals Uniqueness, continuity and the existence of implicit functions in constructive analysis

2011 ◽  
Vol 14 ◽  
pp. 127-136 ◽  
Author(s):  
H. Diener ◽  
P. Schuster
Keyword(s):  
Implicit Function Theorem ◽  
A Priori ◽  
Implicit Function ◽  
Implicit Functions ◽  
Unique Existence ◽  
Constructive Analysis ◽  
Full Proof

AbstractWe extract a quantitative variant of uniqueness from the usual hypotheses of the implicit function theorem. Not only does this lead to an a priori proof of continuity, but also to an alternative, full proof of the implicit function theorem. Additionally, we investigate implicit functions as a case of the unique existence paradigm with parameters.

scholarly journals Implicit Function Theorem. Part II

2019 ◽  
Vol 27 (2) ◽  
pp. 117-131
Author(s):  
Kazuhisa Nakasho ◽  
Yasunari Shidama
Keyword(s):  
Implicit Function Theorem ◽  
Existence And Uniqueness ◽  
Continuous Linear Operator ◽  
Linear Operators ◽  
Implicit Function ◽  
Continuous Linear ◽  
Lipschitz Continuous ◽  
Direct Sum ◽  
Direct Sum Decomposition ◽  
Continuous Linear Operators

Summary In this article, we formalize differentiability of implicit function theorem in the Mizar system [3], [1]. In the first half section, properties of Lipschitz continuous linear operators are discussed. Some norm properties of a direct sum decomposition of Lipschitz continuous linear operator are mentioned here. In the last half section, differentiability of implicit function in implicit function theorem is formalized. The existence and uniqueness of implicit function in [6] is cited. We referred to [10], [11], and [2] in the formalization.

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