Parameter dependence for existence, nonexistence and multiplicity of nontrivial solutions for an Atıcı–Eloe fractional difference Lidstone BVP

• Main Authors: Aijun Yang, Johnny Henderson, Helin Wang
• Format: Article
• Language: English
• Published: University of Szeged 2017-05-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: parameter dependence; atıcı–eloe fractional difference; multiplicity; uniqueness
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5651
• ISSN: 1417-3875; 1417-3875

Dependence on a parameter $\lambda$ are established for existence, nonexistence and multiplicity results for nontrivial solutions to a nonlinear Atıcı–Eloe fractional difference equation $$\Delta^{\nu}y(t-2)-\beta \Delta^{\nu-2}y(t-1) = \lambda f(t+\nu-1,y(t+\nu-1)),$$ with $3 <\nu\leq 4$ a real number, under Lidstone boundary conditions. In particular, the uniqueness of solutions and the continuous dependence of the unique solution on the parameter $\lambda$ are also studied.