THEORY OF DIFFERENCE EQUATIONS Numerical Methods and Applications (Second Edition)

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An extension of Sharkovsky's theorem to periodic difference equations (2006, background): “Although one may find the definitions of various notions of stability of nonautonomous difference systems in many books (see [8,28]), nevertheless we found it pedagogically valuable to simplify these notions for periodic systems.”
Updated semi‐discretization method for periodic delay‐differential equations with discrete delay (2004, background): “Now, the stability investigation is reduced to the problem, whether the eigenvalues of are in modulus less than one [43].”
Multiple homoclinic solutions for the discrete p-Laplacian via critical point theory (2013, positive): “Most of the classicalmethods used in the case of differential equations can be adapted to difference equations, for instance linear and nonlinear operator theory and fixed point theory (for an exhaustive description of the subject, we refer the reader to the monographs of Agarwal [2], Kelley and Pet”
Multiple solutions for discrete boundary value problems (2009, methodology): “Key words and phrases: Difference equations, Discrete p–Laplacian, Variational methods.”