On an Application of a Banach-Steinhaus Theorem to the Study of the Boundedness of Solutions of Non-Linear Differential and Difference Equations

1948 ◽  
Vol 49 (3) ◽  
pp. 515 ◽  
Author(s):  
Richard Bellman
Keyword(s):  
Difference Equations ◽  
Boundedness Of Solutions ◽  
Non Linear ◽  
Linear Differential ◽  
Steinhaus Theorem

scholarly journals Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

scholarly journals A transformation to linearity of some non-linear differential-difference equations

1982 ◽  
Vol 23 (4) ◽  
pp. 416-419
Author(s):  
A. J. Bracken
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Non Linear ◽  
Differential Difference Equation ◽  
Linear Differential

AbstractThe problem of solving a differential-difference equation with quadratic non-linearities of a certain type is reduced to the problem of solving an associated linear differential-difference equation.

scholarly journals Further study on solutions of some non-linear homogeneous differential equations in connection to Brück conjecture

2021 ◽  
Vol 29 (2) ◽  
Author(s):  
DILIP CHANDRA PRAMANIK ◽  
KAPIL ROY
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Linear Differential Equations ◽  
Linear Complex ◽  
Non Linear ◽  
Complex Differential Equations ◽  
Sharing Function ◽  
Linear Differential ◽  
Brück Conjecture

In this paper, using the theory of complex differential equations, we study the solution of some non-linear complex differential equations in connection to Brück conjecture which generalized some earlier results due to Pramanik, D. C. and Biswas, M., On solutions of some non-linear differential equations in connection to Bruck conjecture, Tamkang J. Math., 48 (2017), No. 4, 365–375; and Wang, H., Yang, L-Z. and Xu, H-Y., On some complex differential and difference equations concerning sharing function, Adv. Diff. Equ., 2014, 2014:274.

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