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 -