arXiv subjects
Publications and source records attributed to Julián López-Gómez.
We give a series of very general sufficient conditions in order to ensure the uniqueness of large solutions for --$Δ$u + f (x, u) = 0 in a bounded domain $Ω$ where f : $Ω$ x R $\rightarrow$ R + is a continuous function, such that f (x, 0) = 0 for x $\in$ $Ω$, and f (x, r) > 0 for x in a neighborhood of $\partial$$Ω$ and all r > 0. 2010 Mathematics Subject Classification. 35 J 61; 31 B 15; 28 C 05 .
This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka-Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.
This paper ascertains the global topological structure of the set of subharmonics of arbitrary order of the periodic predator-prey model introduced in López-Gómez, Ortega and Tineo in 1996. By constructing the iterates of the monodromy operator of the system, it is shown that the system admits subharmonics of all orders for the appropriate ranges of values of the parameters. Then, some sharp results of topological nature in the context of global bifurcation theory provide us with the fine topological structure of the components of subharmonics emanating from the T-periodic coexistence state.