A new general forward difference operator and some applications

Abstract

In this study, the forward difference operator is defined in the most general form. As an application we give some criteria on the behavior of solutions of some first-order difference equations involving this operator. To do this, we use a lemma firstly constructed here that gives the relationship between ordinary difference operator and our new operator. Our main theorem improves the known results in the literature, since the potential function in this equation is of a wider function class, including potential functions in equivalent equations existing in the literature. Also some examples are provided to illustrate our main results.

Keywords

• Difference equations,Generalized difference operator,Variable difference operator,Oscillation,Oscillatory

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