Lyapunov-type Inequalities
With Applications to Eigenvalue Problems
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Article
Learning, Mean Field Approximations, and Phase Transitions in Auction Models
In this paper, we study an agent-based model for multi-round, pay as bid, sealed bid reverse auctions using techniques from partial differential equations and statistical mechanics tools. We assume that in eac...
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Article
Inverse nodal problems for singular problems in the half-line
In this paper we study an inverse problem for a singular ordinary differential equation in the half-line. We consider a class of positive weights such that the corresponding eigenvalues do not satisfy a Weyl-t...
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Article
The Fučík Spectrum for One Dimensional Kreĭn–Feller Operators
In this article we study the Fučík spectrum for one dimensional Kreĭn–Feller operators, also known as measure-geometric Laplacians. We show the existence of a sequence of continuous and monotonic curves, and h...
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Article
Open AccessOptimal control for a SIR epidemic model with limited quarantine
Social distance, quarantines and total lock-downs are non-pharmaceutical interventions that policymakers have used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to soci...
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Chapter
A Schelling-Opinion Model Based on Integration of Opinion Formation with Residential Segregation
Residential segregation is a social and economic issue of concern, with implications at the economic, educational, and health levels. Fifty years ago, Schelling introduced a model of interacting agents of two ...
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SIR Dynamics with Vaccination in a Large Configuration Model
We consider an SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, ...
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Coupling Epidemiological Models with Social Dynamics
In this work we study a Susceptible-Infected-Susceptible model coupled with a continuous opinion dynamics model. We assume that each individual can take measures to reduce the probability of contagion, and the...
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Article
A Game Theoretic Model of Wealth Distribution
In this work, we consider an agent-based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero-sum game. Simultaneously, the agents update their way ...
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Article
Homogenization of Fučík Eigencurves
In this work we study the convergence of an homogenization problem for half-eigenvalues and Fučík eigencurves. We provide quantitative bounds on the rate of convergence of the curves for periodic homogenizatio...
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Book
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Chapter
Introduction
In this chapter, we present four theorems that will be proved and generalized in the body of the book. Each one gives a lower bound for the first eigenvalue of a weighted second-order ordinary differential equ...
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Chapter
Nehari–Calogero–Cohn Inequality
In this chapter, we review the proofs of Nehari, Calogero, and Cohn for Theorem C, together with some generalizations for the p-Laplacian eigenvalues and higher-order problems.
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Chapter
Miscellaneous Topics
In this chapter we prove several Lyapunov-type inequalities for systems of ordinary differential equations, one-dimensional nonlinear operators in Orlicz spaces, and quasilinear equations in R ...
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Chapter
Lyapunov’s Inequality
In this chapter we give some proofs of Lyapunov’ inequality, in both the linear and nonlinear contexts.
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Chapter
Bargmann-Type Bounds
In this chapter we study Bargmann-type bounds for the number of negative eigenvalues of Schrödinger equations, which is a well-known hypothesis for the nonoscillatory behavior of solutions of second-order prob...
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Article
Asymptotic of Eigenvalues and Lattice Points
In this work we study the spectral counting function for the p–Laplace operator in one dimension. We show the existence of a two–term Weyl–type asymptote. The method of proof is rather elementary, based on the Di...
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Article
Asymptotic behavior of the eigenvalues of the one-dimensional weightedp-Laplace operator
In this paper we study the spectral counting function for the weightedp-laplacian in one dimension. First, we prove that all the eigenvalues can be obtained by a minimax characterization and then we show the exis...
