Multiple Solutions of a Nonlinear Biharmonic Equation on Graphs
Songbo Hou
Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (4) : 767 -774.
Multiple Solutions of a Nonlinear Biharmonic Equation on Graphs
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.
Locally finite graph / Biharmonic equation / Distinct solutions
| [1] |
|
| [2] |
|
| [3] |
|
| [4] |
|
| [5] |
|
| [6] |
Grigor’yan, A., Lin, Y., Yang, Y.: Yamabe type equations on graphs. J. Differ. Equ. 261, 4924–4943 (2016) |
| [7] |
Grigor’yan, A., Lin, Y., Yang, Y.: Existence of positive solutions to some nonlinear equations on locally finite graphs. Sci. China Math. 60(7), 1311–1324 (2017) |
| [8] |
Grigor’yan, A., Lin, Y., Yang, Y.: Kazdan–Warner equation on graph. Calc. Var. Partial Differ. Equ. 55(4), 1–13 (2016) |
| [9] |
|
| [10] |
|
| [11] |
|
| [12] |
|
| [13] |
|
| [14] |
|
| [15] |
|
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