Bubbling solutions for supercritical problems on manifolds

Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold without boundary and $\Gamma$ be a non degenerate closed geodesic of $(M,g)$. We prove that the supercritical problem $$-\Delta_gu+h u=u^{\frac{n+1}{n-3}\pm\epsilon},\ u>0,\ \hbox{in}\ (M,g)$$ has a solution that concentrates along $\Gamma$ as $\epsilon$ goes to zero, provided the function $h$ and the sectional curvatures along $\Gamma$ satisfy a suitable condition. A connection with the solution of a class of periodic O.D.E.'s with singularity of attractive or repulsive type is established

Generalized Schr\"odinger-Newton system in dimension N≥3N\ge 3: critical case

In this paper we study a system which is equivalent to a nonlocal version of the well known Brezis Nirenberg problem. The difficulties related with the lack of compactness are here emphasized by the nonlocal nature of the critical nonlinear term. We prove existence and nonexistence results of positive solutions when $N=3$ and existence of solutions in both the resonance and the nonresonance case for higher dimensions.Comment: 18 pages, typos fixed, some minor revision

Infinitely many positive solutions for a Schrodinger-Poisson system

We find infinitely many positive non-radial solutions for a nonlinear Schrodinger-Poisson system.Comment: 23 page

Pigment composition of the bright skin in the poison toad, Melanophryniscus rubriventris (Anura: Bufonidae) from Argentina

The determination of the basis of skin colour is important to better understand the evolutionary and ecological relevance of colour variation in aposematic species. Significant variation in bright skin colouration can be found between and within populations of the poison toad, Melanophryniscus rubriventris. In this study, we identified the pigments present in the skin in seven populations of the species in Argentina to determine pigment composition of bright colouration. Our analysis showed that at least four different primary pigments consisting of a suite of orange-red carotenes and yellow xanthophylls contribute to the bright skin colour in different populations of the species. Four carotenoids, Astaxanthin, β-Carotene, Canthaxanthin, and Lycopene were detected by comparison with available standards in skin tissues on each population. Four carotenoids were also detected but not identified. We provide evidence that differences in colouration between individuals and populations in Melanophryniscus rubriventris cannot be merely ascribed to differences in their skin pigment profiles (i.e. pigment types). We discuss alternative explanations and stress the need of more studies on complex mechanisms and interactions affecting the expression of skin colouration in poison frogs and toads.Fil: Bonansea, Maria Ines. Universidad Nacional de Jujuy. Facultad de Ciencias Agrarias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Heit, Cecilia. Universidad Nacional de Jujuy; ArgentinaFil: Vaira, Marcos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Jujuy. Universidad Nacional de Jujuy. Centro de Investigaciones y Transferencia de Jujuy; Argentin

Large mass boundary condensation patterns in the stationary Keller-Segel system

We consider the boundary value problem $-\Delta u + u =\lambda e^u$ in $\Omega$ with Neumann boundary condition, where $\Omega$ is a bounded smooth domain in $\mathbb R^2$, $\lambda>0.$ This problem is equivalent to the stationary Keller-Segel system from chemotaxis. We establish the existence of a solution $u_\lambda$ which exhibits a sharp boundary layer along the entire boundary $\partial\Omega$ as $\lambda\to 0$. These solutions have large mass in the sense that $ \int_\Omega \lambda e^{u_\lambda} \sim |\log\lambda|.