A preliminary treatment of the Central American species of Octoblepharum (Musci: Calymperaceae)

The species of Octoblepharum occurring in Central America have been critically examined. Six are recognized as valid species: O. albidum, O. cocuiense, O. cylindricum, O. erectifolium, O. pulvinatum and O. stramineum. Synonyms are given for these species: O. longifolium = O. albidum; O. mittenii, O. fragillimum, O. pellucidum and =O. pulvinatum var. angustifolium are synonyms of O. cocuiense; O. juruense and O. densum = O. pulvinatum and O. purpureo-brunneum = O. stramineum. All species are widely distributed in the area except for O. cylindricum and O. stramineum that are known only from Belize and Panama respectively.Las especies de Octoblepharum que se presentan en America Central han sido criticamente estudiadas. Se reconocen seis especies: O. albidum, O. cocuiense, O. cylindricum, O. erectifolium, O. pulvinatum y O. stramineum. Se dan los sinonimos para estas especies: O. longifolium = O. albidum; O. fragillimum, O. mittenii, O. pellucidum, O. perforatum y =.O. pulvinatum var. angustifolium son sinonimos de O. cocuiense; O. juruense y O. densum = O. pulvinatum y, O. purpureo-brunneum = O. stramineum. Todas las especies son de amplia distribucion en el area excepto O. cylindricum y O. stramineum que se conocen solo para Belize y Panama respectivamente

Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and energy minimizing partitions

In this paper we consider a stationary Schroedinger operator in the plane, in presence of a magnetic field of Aharonov-Bohm type with semi-integer circulation. We analyze the nodal regions for a class of solutions such that the nodal set consists of regular arcs, connecting the singular points with the boundary. In case of one magnetic pole, which is free to move in the domain, the nodal lines may cluster dissecting the domain in three parts. Our main result states that the magnetic energy is critical (with respect to the magnetic pole) if and only if such a configuration occurs. Moreover the nodal regions form a minimal 3-partition of the domain (with respect to the real energy associated to the equation), the configuration is unique and depends continuously on the data. The analysis performed is related to the notion of spectral minimal partition introduced in [20]. As it concerns eigenfunctions, we similarly show that critical points of the Rayleigh quotient correspond to multiple clustering of the nodal lines.Comment: 32 page

A p-Laplacian supercritical Neumann problem

For $p>2$, we consider the quasilinear equation $-\Delta_p u+|u|^{p-2}u=g(u)$ in the unit ball $B$ of $\mathbb R^N$, with homogeneous Neumann boundary conditions. The assumptions on $g$ are very mild and allow the nonlinearity to be possibly supercritical in the sense of Sobolev embeddings. We prove the existence of a nonconstant, positive, radially nondecreasing solution via variational methods. In the case $g(u)=|u|^{q-2}u$, we detect the asymptotic behavior of these solutions as $q\to\infty$.Comment: 34 pages, 1 figur

Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions

For $1<p<\infty$, we consider the following problem $$-\Delta_p u=f(u),\quad u>0\text{ in }\Omega,\quad\partial_\nu u=0\text{ on }\partial\Omega,$$ where $\Omega\subset\mathbb R^N$ is either a ball or an annulus. The nonlinearity $f$ is possibly supercritical in the sense of Sobolev embeddings; in particular our assumptions allow to include the prototype nonlinearity $f(s)=-s^{p-1}+s^{q-1}$ for every $q>p$. We use the shooting method to get existence and multiplicity of non-constant radial solutions. With the same technique, we also detect the oscillatory behavior of the solutions around the constant solution $u\equiv1$. In particular, we prove a conjecture proposed in [D. Bonheure, B. Noris, T. Weth, {\it Ann. Inst. H. Poincar\'e Anal. Non Lin\'aire} vol. 29, pp. 573-588 (2012)], that is to say, if $p=2$ and $f'(1)>\lambda_{k+1}^{rad}$, there exists a radial solution of the problem having exactly $k$ intersections with $u\equiv1$ for a large class of nonlinearities.Comment: 22 pages, 4 figure

Bryophyte diversity along an altitudinal gradient in Darién National Park, Panama

A bryophyte inventory along an altitudinal gradient on Cerro Pirre (1200 m), Darién National Park, Panama, demonstrates that the different rain forest types along the gradient (inundatedlowland, hillside-lowland, submontane, montane elfin forest) have very different species assemblages. The montane forest has the largest number of exclusive species and the largest bryophyte biomass. Species richness is greatest in the submontane forest. The bryophyte flora of Cerro Pirre is not exceedingly rich in species owing to the rather low elevation of the mountain and the seasonal climate in the adjacent coastal plain. Nevertheless, the distinct altitudinal diversification and the occurrence of a considerable number of rare hepatic taxa, demonstrate the importance of Darién National Park as an area of plant conservation. Forty hepatic species are reported as new to Panama

A priori bounds and multiplicity of positive solutions for pp-Laplacian Neumann problems with sub-critical growth

Let $1<p<+\infty$ and let $\Omega\subset\mathbb R^N$ be either a ball or an annulus. We continue the analysis started in [Boscaggin, Colasuonno, Noris, ESAIM Control Optim. Calc. Var. (2017)], concerning quasilinear Neumann problems of the type -\Delta_p u = f(u), \quad u>0 \mbox{ in } \Omega, \quad \partial_\nu u = 0 \mbox{ on } \partial\Omega. We suppose that $f(0)=f(1)=0$ and that $f$ is negative between the two zeros and positive after. In case $\Omega$ is a ball, we also require that $f$ grows less than the Sobolev-critical power at infinity. We prove a priori bounds of radial solutions, focusing in particular on solutions which start above 1. As an application, we use the shooting technique to get existence, multiplicity and oscillatory behavior (around 1) of non-constant radial solutions.Comment: 26 pages, 3 figure