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| BASIC THEORY OF GENERALIZED $p$-TYPE RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS |
| Liu Yang,Meng Fan,Ravi. P Agarwal |
| (School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun 130024, Jilin, PR China;Department of Mathematics, Texas A$\&$M University-Kingsville, TX78363-8202, Kingsville, TX, USA) |
| DOI： |
| Abstract: |
| A graph $G$ is nonsingular if its adjacency matrix $A(G)$ is nonsingular. A nonsingular graph $G$ is said to have an inverse $G^{+}$ if $A(G)^{-1}$ is signature similar to a nonnegative matrix. Let $\mathcal{H}$ be the class of connected bipartite graphs with unique perfect matchings. We present a characterization of bicyclic graphs in $\mathcal{H}$ which possess unicyclic or bicyclic inverses. |
| Key words: $p$-RFDEs; existence; uniqueness; continuation; continuous dependence on initial value |