scholarly journals QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (IV): FORCED OSCILLATIONS OF HYPERBOLIC TYPE NONLINEAR PARTIAL DIFFERENCE EQUATIONS

1995 ◽  
Vol 26 (4) ◽  
pp. 337-360
Author(s):  
SUI SUN CHENG ◽  
BING GEN ZHANG ◽  
SHENG-LI XIE
Keyword(s):  
Difference Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Hyperbolic Type ◽  
Forced Oscillations ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Oscillation Criteria ◽  
Initial Boundary Value ◽  
Averaging Techniques

Nonlinear hyperbolic type partial difference equations with a forcing term are studied in this paper. By means of two averaging techniques, the problems of oscillation of characteristic initial value problem and of initial boundary value problem are reduced to that of forced and/ or unforced recurrence relations in one variable. A variety of oscillation criteria is given for these relations which in turn yield oscillation criteria for the partial difference equations.

scholarly journals QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (III): FORCED OSCILLATIONS OF PARABOLIC TYPE PARTIAL DIFFERENCE EQUATIONS

1995 ◽  
Vol 26 (2) ◽  
pp. 177-192
Author(s):  
SUI SUN CHENG ◽  
SHENG-LI XIE ◽  
BING-GEN ZHANG
Keyword(s):  
Difference Equations ◽  
Recurrence Relations ◽  
Parabolic Type ◽  
Qualitative Theory ◽  
Forced Oscillations ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Oscillation Criteria ◽  
Forcing Term ◽  
Averaging Techniques

Parabolic type partial difference equations with a forcing term is stud- ied in this paper. By means of three averaging techniques, the problem of oscillation of these equations is reduced to that of recurrence relations in one variable. Avariety of oscillation criteria is given for these recurrence relations which in turn yield oscillation criteria for the partial difference equations.

scholarly journals Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations

2020 ◽  
Vol 100 (4) ◽  
pp. 5-16
Author(s):  
A.T. Assanova ◽  
◽  
Zh.S. Tokmurzin ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Periodic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Hyperbolic Type ◽  
Order System ◽  
Partial Differential ◽  
Initial Boundary Value

A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth-order system of partial differential equations are obtained.

scholarly journals QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (I): OSCILLATION OF NONLINEAR PARTIAL DIFFERENCE EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 279-288
Author(s):  
SUI SUN CHENG ◽  
BING-GEN ZHANG
Keyword(s):  
Difference Equations ◽  
Recurrence Relations ◽  
Qualitative Theory ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Equations With Delay

This paper is concerned with a class of nonlinear partial difference equations with delay. By means of an averaging technique, and several oscillation criteria for ordinary recurrence relations, we are able to establish several oscillation criteria for the partial difference equations.

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