Multiple Solutions of a Nonlinear Biharmonic Equation on Graphs

Songbo Hou

doi:10.1007/s40304-021-00273-4

Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (4) : 767 -774. DOI: 10.1007/s40304-021-00273-4

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Multiple Solutions of a Nonlinear Biharmonic Equation on Graphs

Songbo Hou ¹^,^a

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Abstract

In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph. Using the variation method, we prove that the equation has two distinct solutions under certain conditions.

Keywords

Locally finite graph / Biharmonic equation / Distinct solutions

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Songbo Hou. Multiple Solutions of a Nonlinear Biharmonic Equation on Graphs. Communications in Mathematics and Statistics, 2023, 11(4): 767-774 DOI:10.1007/s40304-021-00273-4