Perturbation results for some nonlinear equations involving fractional operators

By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.Comment: 14 page

Altruism and Selfish Behavior. The Docility Model Revisited

Herbert A. Simon is widely known for his studies on rationality, artificial intelligence and for his pioneering approach to organizational studies. In one of his latest works, he presented a theory of human interaction, focused on the conflict between the selfish and the altruistic that can be seen as the essence of human relationships. The model is quite ambiguous: (1) it follows a kind of social Darwinism that (2) postulates selfish individuals’ extinction. Taking up Simon’s hypotheses on altruism, docility, and selfish behavior, we develop an alternative model of human interaction. The main objective of the paper is to show that rejecting neo-Darwinism and assuming slight complications in the model can explain more in terms of social system interactions. We assume that docility and then altruism, in a technical sense, is the basis of social interaction as it shapes the whole system. It is worth noting that, in the model, selfish individuals do not disappear.docility, altruism, social system, bounded rationality, social interactions, social Darwinism

Soliton dynamics for fractional Schrodinger equations

We investigate the soliton dynamics for the fractional nonlinear Schrodinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation depending of the fractional diffusion parameter.Comment: 22 page

On the location of concentration points for singularly perturbed elliptic equations

By means of a variational identity of Poho\v{z}aev-Pucci-Serrin type for solutions of class $C^1$ recently obtained, we give some necessary conditions for locating the concentration points for a class of quasi-linear elliptic problems in divergence form. More precisely we show that the points where the concentration occurs must be critical, either in a generalized or in the classical sense, for a suitable ground state function.Comment: Final revised version, accepted for publicatio