Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

A new subfamily, Bothriocrotoninae n. subfam., for the genus Bothriocroton Keirans, King & Sharrad, 1994 status amend. (Ixodida : Ixodidae), and the synonymy of Aponomma Neumann, 1899 with Amblyomma Koch, 1844

Evidence suggesting polyphyly of the traditionally recognised tick genus Aponomma Neumann, 1899 is summarized. Continued recognition of this genus in its current concept leaves a polyphyletic genus Aponomma and a paraphyletic genus Amblyomma Koch, 1844. To improve the correlation between our understanding of phylogenetic relationships in metastriate ticks and their classification, a few changes in classification are proposed. The members of the 'indigenous Australian Aponomma' group (sensu Kaufman, 1972), A. auruginans Schulze, 1936, A. concolor Neumann, 1899, A. glebopalma Keirans, King & Sharrad, 1994, A. hydrosauri (Denny, 1843) and A. undatum (Fabricius, 1775), are transferred to Bothriocroton Keirans, King & Sharrad, 1994, which is raised to full generic rank. The remaining members of Aponomma are transferred to Amblyomma. Uncertainty remains on relationships of Bothriocroton to other metastriate lineages and on the systematic position of the two species formerly included in the 'primitive Aponomma' group, A. elaphense Price, 1959 and A. sphenodonti Dumbleton, 1943.