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

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

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

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