Existence of Asymptotic Solutions to Semilinear Partial Difference Equations on Graphs a Research Experience for Undergraduates
نویسندگان
چکیده
This paper studies nonlinear partial difference equations on graphs. We seek solutions to the semilinear equation −Lu + su + u = 0 where L is the Laplacian of a graph G = (V, E). In particular we prove the existence of 3 solutions when s → −∞ and n = |V |. In addition, we find their Morse indices and exact forms. In [4], the authors used the tGNGA method to produce bifurcation diagrams for several graphs; however, these diagrams are not complete. This study complements [4] by using the asymptotic solutions to construct a complete bifurcation diagram.
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تاریخ انتشار 2008