We are concerned with the asymptotic analysis of positive blow-up boundary solutions for a class of quasilinear elliptic equations with an absorption term. By means of the Karamata theory we establish the first two terms in the expansion of the singular solution near the boundary. Our analysis includes large classes of nonlinearities of Keller-Osserman type.
COBISS.SI-ID: 16320089
We prove a generalization of Elkies' characterization of the {\mathbb{Z}}^n lattice to nonunimodular definite forms (and lattices). Combined with inequalities of Frøyshov and of Ozsváth and Szabó, this gives a simple test of whether a rational homology three-sphere may bound a definite four-manifold. As an example we show that small positive surgeries on torus knots do not bound negative-definite four-manifolds.
COBISS.SI-ID: 16408153
We present a topological characterization of LF-spaces and detect small box-products that are (locally) homeomorphic to LF-spaces. This is an important topics from topology of these spaces.
COBISS.SI-ID: 16197465
Using ideas from shape theory we embed the coarse category of metric spaces into the category of direct sequences of simplicial complexes with bonding maps being simplicial. Two direct sequences of simplicial complexes are equivalent if one of them can be transformed to the other by contiguous factorizations of bonding maps and by taking infinite subsequences. This embedding can be realized by either Rips complexes or analogs of Roe's anti-Čech approximations of spaces. In this model coarse n-connectedness of \mathcal{K} = \{K_1 \to K_2 \to \ldots\} means that for each k there is m) k such that the bonding map from K_k to K_m induces trivial homomorphisms of all homotopy groups up to and including n. The asymptotic dimension being at most n means that for each k there is m ) k such that the bonding map from K_k to K_m factors (up to contiguity) through an n-dimensional complex. Property A of G. Yu is equivalent to the condition that for each k and for each \epsilon ) 0 there is m ) k such that the bonding map from \vert K_k \vert to \vert K_m \vert has a contiguous approximation g \colon \vert K_k \vert \to \vert K_m \vert which sends simplices of \vert K_k \vert to sets of diameter at most \epsilon.
COBISS.SI-ID: 16094809
We are concerned with the Lane-Emden-Fowler equation -\Delta = \lambda k(x)u^q \pm h(x)u^p in \Omega, subject to the Dirichlet boundary condition u=0 on \partial \Omega, where \Omega is a smooth bounded domain in {\mathbb R}^N, k and h are variable potential functions, and 0(q(1(p. Our analysis combines monotonicity methods with variational arguments.
COBISS.SI-ID: 16090201