Peano's Existence Theorem revisited

We present new proofs to four versions of Peano's Existence Theorem for ordinary differential equations and systems. We hope to have gained readability with respect to other usual proofs. We also intend to highlight some ideas due to Peano which are still being used today but in specialized contexts: it appears that the lower and upper solutions method has one of its oldest roots in Peano's paper of 1886

Existence of minimal and maximal solutions to first--order differential equations with state--dependent deviated arguments

We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the unknown solutions. Our existence results lean on new definitions of lower and upper solutions introduced in this paper, and we show with an example that similar results with the classical definitions are false. We also introduce an example showing that the problems considered need not have the least (or the greatest) solution between given lower and upper solutions, but we can prove that they do have minimal and maximal solutions in the usual set--theoretic sense. Sufficient conditions for the existence of lower and upper solutions, with some examples of application, are provided too

Powers in the Lucas sequence when the index is divisible by three

In this paper the m-powers with m ≥ 2 included in the Lucas sequences when the index satisfies some conditions are foun

First report of Delphastus quinculus Gordon and Diomus seminulus (Mulsant) (Coleoptera: Coccinellidae) feeding on eggs and first-instar nymphs of Crypticerya multicicatrices Kondo and Unruh (Hemiptera: Monophlebidae)

Delphastus quinculus Gordon and Diomus seminulus (Mulsant) (Coleoptera: Coccinellidae) are reported for the first time feeding on eggs and first-instar nymphs of Crypticerya multicicatrices Kondo and Unruh (Hemiptera: Monophlebidae). Diagnosis and illustrations are provided for both species. Updated information on their biology, hosts and geographical distribution is also provided.Se reportan a Delphastus quinculus Gordon y Diomus seminulus (Mulsant) (Coleoptera: Coccinellidae) por primera vez como depredadores de huevos y ninfas del primer instar de Crypticerya multicicatrices Kondo and Unruh (Hemiptera: Monophlebidae). Las dos especies de coccinélidos se diagnostican y se ilustran en detalle. Se provee también información actualizada sobre sus biologías, hospederos y distribución geográfica

La solución extrajudicial de conflictos laborales en el modelo español: a medio camino entre el desiderátum legal y el ostracismo social

El ordenamiento laboral ha apostado tradicionalmente por tratar de conseguir que los conflictos surgidos de forma casi genética en el seno de las relaciones de trabajo sean resueltos por cauces compositivos que eviten, en lo posible, la vía judicial.El presente trabajo recorre las diversas vías de solución extrajudicial de conflictos que se han arbitrado en el sistema español, efectuando una valoración positiva de las intenciones, pero destacando también las críticas que, en su funcionamiento práctico, el modelo merece.The labour law has bet traditionally for trying to get that the conflicts arisen in the labour relations are solved by extrajudicial ways in orther to avoid, as much as possible, the judicial way. The present work crosses the diverse routes of extrajudicial solution of conflicts that have been arbitrated in the Spanish system, giving a positive valuation of the intentions, but emphasizing also the critiques of the Spanish model