Abstract
We investigate the existence of positive solutions for a nonlinear second-order difference equation with a linear term and a sign-changing nonlinearity, supplemented with multi-point boundary conditions. In the proof of our main results, we use the Guo–Krasnosel'skii fixed point theorem.
Highlights
We investigate the existence of positive solutions for a nonlinear second-order difference equation with a linear term and a sign-changing nonlinearity, supplemented with multi-point boundary conditions
The existence, nonexistence and multiplicity of positive solutions for difference equations and systems of difference equations with parameters or without parameters, with nonnegative or sign-changing nonlinearities, supplemented with various boundary conditions were investigated in the papers [1, 3–6, 8–10, 12, 14–17, 21–23] and the monograph [13]
We study the second-order difference equation
Summary
Under some assumptions on the function f , we will investigate the existence of at least one or two positive solutions for problem (E)–(BC). Equation (E) with L = 0, where the nonlinearity f may be unbounded below or nonpositive, subject to the boundary conditions u0 = u1 and uN = uN−1, which is a resonant problem, has been investigated in the paper [7] by transforming it into c 2019 Author. The existence, nonexistence and multiplicity of positive solutions for difference equations and systems of difference equations with parameters or without parameters, with nonnegative or sign-changing nonlinearities, supplemented with various boundary conditions were investigated in the papers [1, 3–6, 8–10, 12, 14–17, 21–23] and the monograph [13]. For various applications of the nonlinear difference equations in many domains, we recommend the readers the monographs [2], [18] and [19]
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