Semilinear problems at resonance with nonlinearities depending only on the derivative

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGWe deal with second-order semilinear equations with a nonlinear term depending only on the derivative. Our main results extend or complement some previous work by J. MawhinAgencia Estatal de Investigación | Ref. PID2021-122442-10

The full power of the half-power

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGWe use the complex square root to define a very simple homotopic invariant over the non-vanishing functions defined on the circle. As a consequence we provide easy proofs of the plane Brouwer fixed point theorem and the Fundamental Theorem of Algebra. The relation of this new invariant with the winding number and the Brouwer degree will be fully unveiledAgencia Estatal de Investigación | Ref. PID2021-122442NB-10

The Brouwer fixed point theorem and periodic solutions of differential equations

The Brouwer fixed point theorem is a key ingredient in the proof that a periodic differential equation has a periodic solution in a set that satisfies a suitable tangency condition on its boundary. The main goal of this note is to show that both results are in fact equivalent.Universidade de Vigo/CISUGAgencia Estatal de Investigación | Ref. MTM2017-85054-C2-1-

Existence and multiplicity of solutions for a periodic hill’s equation with parametric dependence and singularities

We deal with the existence and multiplicity of solutions for the periodic boundary value problem positive parameter. The function f : is allowed to be singular, and the related Green’s function is nonnegative and can vanish at some points.This work was partially supported by FEDER and Ministerio de Educacion y Ciencia, Spain, project no. MTM2010-15314S

New Lipschitz–type conditions for uniqueness of solutions of ordinary differential equations

We present some generalized Lipschitz conditions which imply uniqueness of solutions for scalar ODEs. We illustrate the applicability of our results with examples not covered by earlier Lipschitz–type uniqueness testsRodrigo López Pouso and Jorge Rodríguez López were partially supported by grant ED431C 2019/02, Xunta de Galicia (Spain), and by Ministerio de Ciencia y Tecnología (Spain), grant PID2020-113275GB-I00S

Clonal chromosomal mosaicism and loss of chromosome Y in elderly men increase vulnerability for SARS-CoV-2

The pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, COVID-19) had an estimated overall case fatality ratio of 1.38% (pre-vaccination), being 53% higher in males and increasing exponentially with age. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, we found 133 cases (1.42%) with detectable clonal mosaicism for chromosome alterations (mCA) and 226 males (5.08%) with acquired loss of chromosome Y (LOY). Individuals with clonal mosaic events (mCA and/or LOY) showed a 54% increase in the risk of COVID-19 lethality. LOY is associated with transcriptomic biomarkers of immune dysfunction, pro-coagulation activity and cardiovascular risk. Interferon-induced genes involved in the initial immune response to SARS-CoV-2 are also down-regulated in LOY. Thus, mCA and LOY underlie at least part of the sex-biased severity and mortality of COVID-19 in aging patients. Given its potential therapeutic and prognostic relevance, evaluation of clonal mosaicism should be implemented as biomarker of COVID-19 severity in elderly people. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, individuals with clonal mosaic events (clonal mosaicism for chromosome alterations and/or loss of chromosome Y) showed an increased risk of COVID-19 lethality

A positive fixed point theorem with applications to systems of Hammerstein integral equations

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results.Ministerio de Ciencia e Innovación | Ref. MTM2010-15314Ministerio de Economía y Competitividad | Ref. MTM2013-43014-

Existence results for damped regular equations under periodic or Neumann boundary conditions

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGWe present a version of the averaging and a method to construct lower and upper solutions in the reversed order that are suitable for both the periodic and the Neumann boundary conditions. As an application, we obtain new results for a periodic problem related to the Liebau phenomenon and for a Neumann boundary value problem arising in fluid dynamics