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.

scholarly journals QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (II): OSCILLATION CRITERIA FOR DIRECT CONTROL SYSTEMS IN SEVERAL VARIABLES

1995 ◽  
Vol 26 (1) ◽  
pp. 65-79
Author(s):  
SUI SUN CHENG ◽  
SHENG-LI XIE ◽  
BING-GEN ZHANG
Keyword(s):  
Control Systems ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Qualitative Theory ◽  
Direct Control ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Several Variables

This paper is concerned with several direct control systems which are described by partial difference equations. By means of an averaging technique and several oscillation criteria for ordinary recurrence relations, we are able to establish several oscillation criteria for these control systems.

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 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.

On some Sum-Difference Inequalities and Applications to Boundary Value Problems

2012 ◽  
Vol 450-451 ◽  
pp. 696-700
Author(s):  
Bao Ju Sun ◽  
Ye Bao
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Boundary Value ◽  
Qualitative Theory ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Explicit Bounds

The aim of the present paper is to establish some new sum-difference inequalities which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial difference equations

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