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Existence And Multiplicity Of Positive Solutions For Discrete Anisotropic Equations, Marek Galewski, Renata Wieteska

Turkish Journal of Mathematics

In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function \alpha , a nonlinear term f, and a numerical parameter \lambda :\Delta (\alpha (k) \Delta u(k-1) ^{p(k-1)-2}\Delta u(k-1)) + \lambda f(k,u(k))=0, k\in [1,T] . We derive the intervals of a numerical parameter \lambda for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived.