| Abstract: |
| This talk deals with the analysis of 1-node solutions of the diffusive logistic equation. We first present the numerical simulations carried out in a recent paper concerning these solutions for a class of non-degenerate, or classical, diffusive logistic equation. Then, we present a substantial refinement of a multiplicity result of J. L\`{o}pez-G\`{o}mez and P. H. Rabinowitz. According to it, we can construct diffusive classical logistic equations with an arbitrarily large number of 1-node solutions for the appropriate ranges of values of the parameters. It is the first multiplicity result of this nature available in the literature. Finally, we describe numerically the global structure of this set of solutions for the degenerate case. Our main findings reveal that the number of such nodal solutions, as well as the number of components in the bifurcation diagrams, strongly depends on the number and position of the set components where the weight function in front of the nonlinearity vanishes. No technical device seems to be available to deal analytically with these problems. |
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