A generalization of the Schauder fixed point theorem via multivalued contractions

summary:We establish a fixed point theorem for a continuous function $f:X\to E$, where $E$ is a Banach space and $X\subseteq E$. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented

Infinitely many solutions for a boundary value problem with impulsive effects

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Two positive solutions for nonlinear fourth-order elastic beam equations

The aim of this paper is to study the existence of at least two non-trivial solutions to a boundary value problem for fourth-order elastic beam equations given by u (4) + Au00 + Bu = λ f(x, u) in [0, 1], u(0) = u(1) = 0, u 00(0) = u 00(1) = 0, under suitable conditions on the nonlinear term on the right hand side. Our approach is based on variational methods, and in particular, on an abstract two critical points theorem given for differentiable functionals defined on a real Banach space

Prolonged higher dose methylprednisolone vs. conventional dexamethasone in COVID-19 pneumonia: a randomised controlled trial (MEDEAS)

Dysregulated systemic inflammation is the primary driver of mortality in severe COVID-19 pneumonia. Current guidelines favor a 7-10-day course of any glucocorticoid equivalent to dexamethasone 6 mg·day-1. A comparative RCT with a higher dose and a longer duration of intervention was lacking