Abstract
Concerned is the existence, nonexistence and multiplicity of positive solutions for discrete ϕ-Laplacian eigenvalue problems. By using lower and upper solutions method and fixed point index theory, a global result with respect to parameter is established.
Highlights
B ∈ Z with a < b, let [a, b]Z = {a, a +, a +, . . . , b, b}
To the best of our knowledge, there are no results on the existence and multiplicity of positive solutions for difference φ-Laplacian problems
The result is motivated mainly by the ideas in [, ], in which some global results of positive solutions were established for boundary value problems of p-Laplacian differential systems and φ-Laplacian differential systems, respectively
Summary
We consider the following discrete φ-Laplacian eigenvalue problem (φ( u(k – ))) + λp(k)g(u(k)) = , k ∈ [ , T]Z,. The differential φ-Laplacian problems have been widely studied in many different papers. For discrete φ-Laplacian problems, there are less study results than differential φLaplacian problems. To the best of our knowledge, there are no results on the existence and multiplicity of positive solutions for difference φ-Laplacian problems. The purpose of this paper is to establish a global result of positive solutions of ( ). The result is motivated mainly by the ideas in [ , ], in which some global results of positive solutions were established for boundary value problems of p-Laplacian differential systems and φ-Laplacian differential systems, respectively.
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