Some techniques on nonlinear analysis and applications

In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second result, more technical, but also connected to the first one, is an extension of the well-known Pietsch Domination Theorem. The last decade witnessed the birth of different families of Pietsch Domination-type results and some attempts of unification. Our result, that we call "full general Pietsch Domination Theorem" is potentially a definitive Pietsch Domination Theorem which unifies the previous versions and delimits what can be proved in this line.The connections to the recent notion of weighted summability are traced.Comment: 24 page

A general Extraplolation Theorem for absolutely summing operators

In this note we prove a general version of the Extrapolation Theorem, extending the classical linear extrapolation theorem due to B. Maurey. Our result shows, in particular, that the operators involved do not need to be linear

Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this paper to improve the constants for vector-valued Bohnenblust--Hille type inequalities.Comment: 16 page

Existence and exponential stability of periodic solutions of Nicholson-type systems with nonlinear density-dependent mortality and linear harvesting

In this work we study a Nicholson-type periodic system with variable delay, density-dependent mortality and linear harvesting rate. Using the topological degree and Lyapunov stability theories, we obtain sufficient conditions that allow us to demonstrate the existence of periodic solutions for the Nicholson-type system and, under suitable conditions, the uniqueness and local exponential stability of the periodic solution is established. We illustrate our results with an example and numerical simulations