MULTIPLE POSITIVE SOLUTIONS FOR DISCRETE p-LAPLACIAN EQUATIONS WITH POTENTIAL TERM

We study the existence of solutions to nonlinear discrete boundary value problems with the discrete p-Laplacian, potential, and nonlinear source terms. Using variational methods, we demonstrate that there exist at least two positive solutions. The existence strongly depends on the smallest positive...

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Bibliographic Details
Published in:Applicable analysis and discrete mathematics 2013-10, Vol.7 (2), p.327-342
Main Authors: Kim, Jong-Ho, Park, Jea-Hyun, Lee, June-Yub
Format: Article
Language:English
Subjects:
Boundary value problems
Critical points
Eigenfunctions
Eigenvalues
Induced subgraphs
Mathematical functions
Vertices
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Summary:We study the existence of solutions to nonlinear discrete boundary value problems with the discrete p-Laplacian, potential, and nonlinear source terms. Using variational methods, we demonstrate that there exist at least two positive solutions. The existence strongly depends on the smallest positive eigenvalue of Dirichlet eigenvalue problems and the growth conditions of the source terms.
ISSN:1452-8630
2406-100X
DOI:10.2298/AADM130612012K