On the system of anisotropic discrete BVPs

Existence and multiplicity of positive solutions for discreteanisotropic equationsExistence and multiplicity of positive solutions for discreteanisotropic equations

“…⟨J ′ λ (u), v⟩ = 0 for all v ∈ H . Summing by parts and taking boundary values into account, see [10], we observe that…”

An Existence Result for Discrete Anisotropic Equations

“…Secondly, they derived some version of a discrete three critical point theorem which they applied in order to get the existence of at least two nontrivial solutions. Galewski and Wieteska in [10], studied the existence of solutions of a system of anisotropic discrete boundary value problems using critical point theory, while in [? ], they derived the intervals of the numerical parameter for which the parametric version of the problem (1.1) has at least 1, exactly 1, or at least 2 positive solutions.…”

A Variational Approach to Perturbed Discrete Anisotropic Equations

“…On the other hand, numerous researches have been undertaken on the existence of solutions for discrete anisotropic boundary value problems (BVPs) in recent years. As to the background and latest results, the readers can refer to [32][33][34][35][36][37][38] and the references therein. For example, Mihȃilescu et al in [36], by using critical point theory, obtained the existence of a continuous spectrum for a family of discrete boundary value problems.…”

“…For example, Mihȃilescu et al in [36], by using critical point theory, obtained the existence of a continuous spectrum for a family of discrete boundary value problems. Galewski and Wieteska in [34] investigated the existence of solutions of the system of anisotropic discrete boundary value problems using critical point theory, while in [33], using variational methods, they derived the intervals of the numerical parameter for which the problem ( , ) has at least 1, exactly 1, or at least 2 positive solutions. They also derived some useful discrete inequalities.…”