Geodesic
Infinite Schrödinger networks
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 4, pp. 640-650 Cet article a éte moissonné depuis la source Math-Net.Ru

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Finite-difference models of partial differential equations such as Laplace or Poisson equations lead to a finite network. A discretized equation on an unbounded plane or space results in an infinite network. In an infinite network, Schrödinger operator (perturbed Laplace operator, $q$-Laplace) is defined to develop a discrete potential theory which has a model in the Schrödinger equation in the Euclidean spaces. The relation between Laplace operator $\Delta$-theory and the $\Delta_q$-theory is investigated. In the $\Delta_q$-theory the Poisson equation is solved if the network is a tree and a canonical representation for non-negative $q$-superharmonic functions is obtained in general case.
Keywords: $q$-harmonic functions, $q$-superharmonic functions, Schrödinger network, hyperbolic Schrödinger network, parabolic Schrödinger network, integral representation. 
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N. Nathiya; Ch. Amulya Smyrna. Infinite Schrödinger networks. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 4, pp. 640-650. http://geodesic.mathdoc.fr/item/VUU_2021_31_4_a7/

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