TY - JOUR
T1 - Zeros of solutions of functional equations in the space of discontinuous functions of two variables
AU - Domoshnitsky, Alexander
PY - 2005/8/15
Y1 - 2005/8/15
N2 - In this paper distribution of zeros of solutions of functional equations in the space of functions of two variables is studied. A zero of a solution in the space of noncontinuous functions is defined. It is demonstrated that oscillatory properties of functional equations are determined by the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Zones of solution positivity are estimated. Various exact oscillation and non-oscillation tests are proposed. A necessary and sufficient condition of oscillation is obtained.
AB - In this paper distribution of zeros of solutions of functional equations in the space of functions of two variables is studied. A zero of a solution in the space of noncontinuous functions is defined. It is demonstrated that oscillatory properties of functional equations are determined by the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Zones of solution positivity are estimated. Various exact oscillation and non-oscillation tests are proposed. A necessary and sufficient condition of oscillation is obtained.
KW - Difference equations
KW - Oscillation and nonoscillation
KW - Zeros of solution
KW - Zones of positivity
UR - http://www.scopus.com/inward/record.url?scp=20744443660&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2004.11.056
DO - 10.1016/j.jmaa.2004.11.056
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AN - SCOPUS:20744443660
SN - 0022-247X
VL - 308
SP - 656
EP - 668
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -