Multiple positive solutions for discrete p-laplacian equations with potential term

Jong Ho Kim; Jea Hyun Park; June Yub Lee

doi:10.2298/AADM130612012K

Multiple positive solutions for discrete p-laplacian equations with potential term

Jong Ho Kim, Jea Hyun Park, June Yub Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study the existence of solutions to nonlinear discrete boundary value prob- lems with the discrete p-Laplacian, potential, and nonlinear source terms. Us- ing 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.

Original language	English
Pages (from-to)	327-342
Number of pages	16
Journal	Applicable Analysis and Discrete Mathematics
Volume	7
Issue number	2
DOIs	https://doi.org/10.2298/AADM130612012K
State	Published - 2013

Keywords

Discrete boundary value problems
Discrete p-Laplacian
Graph Laplacian
Multiple solutions

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10.2298/AADM130612012K

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title = "Multiple positive solutions for discrete p-laplacian equations with potential term",

abstract = "We study the existence of solutions to nonlinear discrete boundary value prob- lems with the discrete p-Laplacian, potential, and nonlinear source terms. Us- ing 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.",

keywords = "Discrete boundary value problems, Discrete p-Laplacian, Graph Laplacian, Multiple solutions",

author = "Kim, {Jong Ho} and Park, {Jea Hyun} and Lee, {June Yub}",

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AU - Kim, Jong Ho

AU - Park, Jea Hyun

AU - Lee, June Yub

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AB - We study the existence of solutions to nonlinear discrete boundary value prob- lems with the discrete p-Laplacian, potential, and nonlinear source terms. Us- ing 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.

KW - Discrete boundary value problems

KW - Discrete p-Laplacian

KW - Graph Laplacian

KW - Multiple solutions

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DO - 10.2298/AADM130612012K

M3 - Article

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VL - 7

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EP - 342

JO - Applicable Analysis and Discrete Mathematics

JF - Applicable Analysis and Discrete Mathematics

IS - 2

ER -

Multiple positive solutions for discrete p-laplacian equations with potential term

Abstract

Keywords

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