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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Existence And Multiplicity Of Positive Solutions For Discrete Anisotropic Equations, Marek Galewski, Renata Wieteska
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.
Gradient Estimates For The Porous Medium Type Equation On Smooth Metric Measure Space, Deng Yihua
Gradient Estimates For The Porous Medium Type Equation On Smooth Metric Measure Space, Deng Yihua
Turkish Journal of Mathematics
The porous medium equation arises in different applications to model diffusive phenomena. In this paper, we obtain several gradient estimates for some porous medium type equations on smooth metric measure space with N-Bakry-Emery Ricci tensor bounded from below. In particular, we improve and generalize some current gradient estimates for the porous medium equations.