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An analysis of nonlocal difference equations with finite convolution coefficients

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Abstract

Existence of at least one positive solution to the second-order nonlocal difference equation

$$\begin{aligned} -A\Big (\big (a*(g\circ u)\big )(b)\Big )\big (\Delta ^2u\big )(n)=\lambda f\big (n,u(n+1)\big ), \end{aligned}$$

where \((a*u)(b)\) represents a finite convolution and \(g\circ u\) denotes the composition of the functions g and u, is considered subject to Dirichlet boundary conditions. Since we use a specially tailored order cone, we are able to introduce minimal conditions on the coefficient function A.

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    Christopher S. Goodrich

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Goodrich, C.S. An analysis of nonlocal difference equations with finite convolution coefficients. J. Fixed Point Theory Appl. 24, 1 (2022). https://doi.org/10.1007/s11784-021-00914-9

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