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.

scholarly journals On solutions of some non-linear differential equations in connection to Bruck Conjecture

2017 ◽  
Vol 48 (4) ◽  
pp. 365-375
Author(s):  
Dilip Candra Pamanik ◽  
Manab Biswas
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
Linear Complex ◽  
Non Linear ◽  
Complex Differential Equations ◽  
Linear Differential ◽  
Brück Conjecture

In this paper, we investigate on the non-constant entire solutions of some non-linear complex differential equations in connection to Br\"{u}ck conjecture and prove some results which improve and extend the results of Xu and Yang\bf{[Xu HY, Yang LZ. On a conjecture of R. Br\"{u}ck and some linear differential equations. Springer Plus 2015; 4:748,:1-10, DOI 10.1186/s40064-015-1530-5.]}

Further study on the Brück conjecture and some non-linear complex differential equations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Dilip Chandra Pramanik ◽  
Kapil Roy
Keyword(s):  
Differential Equations ◽  
Current Paper ◽  
Small Function ◽  
Entire Solutions ◽  
Linear Complex ◽  
Content Type ◽  
Complex Differential Equation ◽  
Non Linear ◽  
Complex Differential Equations ◽  
Brück Conjecture

PurposeThe purpose of this current paper is to deal with the study of non-constant entire solutions of some non-linear complex differential equations in connection to Brück conjecture, by using the theory of complex differential equation. The results generalize the results due to Pramanik et al.Design/methodology/approach39B32, 30D35.FindingsIn the current paper, we mainly study the Brück conjecture and the various works that confirm this conjecture. In our study we find that the conjecture can be generalized for differential monomials under some additional conditions and it generalizes some works related to the conjecture. Also we can take the complex number a in the conjecture to be a small function. More precisely, we obtain a result which can be restate in the following way: Let f be a non-constant entire function such that σ2(f)<∞, σ2(f) is not a positive integer and δ(0, f)>0. Let M[f] be a differential monomial of f of degree γM and α(z), β(z)∈S(f) be such that max{σ(α), σ(β)} <σ(f). If M[f]+β and fγM−α share the value 0 CM, then M[f]+βfγM−α=c,where c≠0 is a constant.Originality/valueThis is an original work of the authors.

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

scholarly journals Pendulum with aerodynamic and viscous damping

2020 ◽  
Vol 3 (2) ◽  
pp. 43-47
Author(s):  
Herlin Soraya
Keyword(s):  
Differential Equations ◽  
Stable State ◽  
The State ◽  
Linear Differential Equations ◽  
Viscous Damping ◽  
Viscous Damper ◽  
Aerodynamic Damping ◽  
Non Linear ◽  
Linear Differential ◽  
The Relationship

In this paper we discuss about how the relationship between non-linear differential equations on aerodynamic damping with linearly viscous damping equations. And it turns out after analyzing that the changes that occur pendulum that changes from the start of the maximum state to a stable state takes time so that changes that occur until the state is stable, this change can be reduced with the use of viscous damper

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.

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