scholarly journals Periodic solutions of certain nonlinear parabolic differential equations in domains with periodically moving boundaries

1978 ◽  
Vol 70 ◽  
pp. 111-123 ◽  
Author(s):  
Yoshio Yamada
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Moving Boundaries ◽  
Typical Problem ◽  
Parabolic Differential Equations ◽  
Periodic Problems ◽  
Nonlinear Parabolic

In this paper we consider the periodic problems for certain nonlinear parabolic differential equations in domains with periodically moving boundaries. The typical problem, which is going to be discussed in the present paper, is to solve the following:

scholarly journals Existence for Singular Periodic Problems: A Survey of Recent Results

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Jifeng Chu ◽  
Juntao Sun ◽  
Patricia J. Y. Wong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Impulsive Differential Equations ◽  
Differential Systems ◽  
Singular Differential Equations ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.

scholarly journals On Some regularity properties for solutions of nonlinear parabolic differential equations

1992 ◽  
Vol 128 ◽  
pp. 49-63 ◽  
Author(s):  
Haruo Nagase
Keyword(s):  
Differential Equations ◽  
Bounded Domain ◽  
Open Interval ◽  
Function Spaces ◽  
Parabolic Differential Equations ◽  
Regularity Properties ◽  
Nonlinear Parabolic ◽  
Class C

Let G be a bounded domain in Rn with coordinates x = (x1,…,xn) and let its boundary S be of class C2. We assume that the usual function spaces Lq(G), Wl, q(G) and are known. We write the norm of Lq(G) by | |q and the adjoint number of q by q*, i.e., q* = q/(q —1).For any positive number T we denote the open interval (0,T) by I, the cylinder G X I in Rn+1 by Q and the norm of Lq(Q) by ‖ ‖q.

scholarly journals A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 677 ◽  
Author(s):  
Kadry ◽  
Alferov ◽  
Ivanov ◽  
Korolev ◽  
Selitskaya
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Lower Bounds ◽  
New Method ◽  
Upper And Lower Bounds ◽  
First Order ◽  
Periodic Problems ◽  
Existence And Stability

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

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