A discrete fourth-order Lidstone problem with parameters

Various existence, multiplicity, and nonexistence results for nontrivial solutions to a nonlinear discrete fourth-order Lidstone boundary value problem with dependence on two parameters are given, using a symmetric Green’s function approach. An existence result is also given for a related semipositone problem, thus relaxing the usual assumption of nonnegativity on the nonlinear term

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