Existence and multiplicity results for boundary value problems connected with the discrete p(·)−Laplacian on weighted finite graphs

Marek Galewski and Renata Wieteska

Applied Mathematics and Computation, 2016, vol. 290, issue C, 376-391

Abstract: We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush–Kuhn–Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the discrete p(·)−Laplacian on weighted finite graphs. Several auxiliary inequalities for the discrete p(·)−Laplacian on finite graphs are also derived. Positive solutions are considered.

Keywords: Weighted graph; p(·)−Laplacian on a graph; Critical point theory; Existence and multiplicity (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:290:y:2016:i:c:p:376-391

DOI: 10.1016/j.amc.2016.06.016

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