When is stability in the eye of the beholder? Comments on a singular initial-value problem for a nonlinear differential equation arising in semiclassical cosmology

1990 ◽  
Vol 42 (12) ◽  
pp. 4248-4250 ◽  
Author(s):  
S. A. Fulling
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Initial Value Problem ◽  
Initial Value ◽  
Singular Initial Value Problem

An iteration method for a nonlinear differential equation describing the convergence to equilibrium in a system of reacting polymers

1981 ◽  
Vol 375 (1763) ◽  
pp. 529-542
Keyword(s):  
Differential Equation ◽  
Initial Data ◽  
Global Solution ◽  
Nonlinear Differential Equation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Constructive Method ◽  
Convergence To Equilibrium ◽  
Initial Value

A constructive method is presented to give the global solution to a nonlinear initial value problem describing the convergence to equilibrium in a system of reacting polymers. The solution is proved to be unique and continuous with respect to small variations in the initial data.

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

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