Sufficient conditions for the existence of heteroclinic solutions for Phi-Laplacian differential equations

In this paper we consider the second order discontinuous equation in the real line, (a(t)φ(u′(t)))′ = f(t,u(t),u′(t)), a.e.t∈R, u(-∞) = ν⁻, u(+∞)=ν⁺, with φ an increasing homeomorphism such that φ(0)=0 and φ(R)=R, a∈C(R,R\{0})∩C¹(R,R) with a(t)>0, or a(t)<0, for t∈R, f:R³→R a L¹-Carathéodory function and ν⁻,ν⁺∈R such that ν⁻<ν⁺. We point out that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities φ and f. Moreover, as far as we know, this result is even new when φ(y)=y, that is, for equation (a(t)u′(t))′=f(t,u(t),u′(t)), a.e.t∈R.

Effects of flow regulation in the life-cycles of a mediterranean cyprinid species, the Iberian chub (Squalius carolitertii Doadrio, 1987)

Streamflow is considered a driver of inter and intra‐specific life‐history differences among freshwater fish. Therefore, dams and related flow regulation, can have deleterious impacts on their life‐cycles. The main objective of this study is to assess the effects of flow regulation on the growth and reproduction of a non‐migratory fish species. During one year, samples were collected from two populations of Iberian chub, inhabiting rivers with non‐regulated and regulated flow regimes. Flow regulation for water derivation promoted changes in chub’s condition, duration of gonad maturation and spawning, fecundity and oocyte size. However, this non‐migratory species was less responsive to streamflow regulation than a migratory species analysed. Findings from this study are important to understand changes imposed by regulated rivers on fish and can be used as guidelines for flow requirements implementations; RESUMO: O caudal é um dos fatores responsáveis pelo funcionamento dos ciclos de vida das espécies piscícolas dulciaquícolas. As barragens, e a regularização de caudal associada, podem ter impactes nos ciclos de vida destas espécies. O objetivo deste estudo prende‐se com a avaliação dos efeitos da regularização de caudal no crescimento e reprodução de uma espécie piscícola não‐migradora. A análise de amostras recolhidas em populações de escalo do Norte provenientes de dois rios de caudal regularizado e não regularizado, identificaram impactes significativos a nível da condição corporal, da maturação das gónadas e desova, da fecundidade e da dimensão dos oócitos. Esta espécie não‐migradora parece ser menos responsiva à artificialização do caudal que uma espécie migradora previamente analisada. Estes resultados permitem compreender as alterações impostas pela regularização do caudal e podem ser usados em programas de reabilitação fluvial.