Decaying solutions for discrete boundary value problems on the half line

• Published in: Journal of difference equations and applications Vol. 22; no. 9; pp. 1244 - 1260
• Main Authors: Došlá, Zuzana, Marini, Mauro, Matucci, Serena
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01-09-2016; Taylor & Francis Ltd
• Subjects: Applied mathematics; Boundary value problems; Decay; decaying solutions; Difference equations; Differential equations; fixed point theorems in Fréchet spaces; Fixed points (mathematics); functional equations; Mathematical analysis; p-Laplacian difference equations; recessive solutions; Theorems
• ISSN: 1023-6198; 1563-5120
• DOI: 10.1080/10236198.2016.1190349

Some nonlocal boundary value problems, associated to a class of functional difference equations on unbounded domains, are considered by means of a new approach. Their solvability is obtained by using properties of the recessive solution to suitable half-linear difference equations, a half-linearization technique and a fixed point theorem in Frechét spaces. The result is applied to derive the existence of nonoscillatory solutions with initial and final data. Examples and open problems complete the paper.