18,152 research outputs found
Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems
We prove the existence of positive periodic solutions for the second order
nonlinear equation , where has superlinear growth at
zero and at infinity. The weight function is allowed to change its sign.
Necessary and sufficient conditions for the existence of nontrivial solutions
are obtained. The proof is based on Mawhin's coincidence degree and applies
also to Neumann boundary conditions. Applications are given to the search of
positive solutions for a nonlinear PDE in annular domains and for a periodic
problem associated to a non-Hamiltonian equation.Comment: 41 page
On a diffusion model with absorption and production
We discuss the structure of radial solutions of some superlinear elliptic
equations which model diffusion phenomena when both absorption and production
are present. We focus our attention on solutions defined in R (regular) or in R
\ {0} (singular) which are infinitesimal at infinity, discussing also their
asymptotic behavior. The phenomena we find are present only if absorption and
production coexist, i.e., if the reaction term changes sign. Our results are
then generalized to include the case where Hardy potentials are considered
Bifurcating solutions of the Lichnerowicz equation
We give an exhaustive description of bifurcations and of the number of
solutions of the vacuum Lichnerowicz equation with positive cosmological
constant on with -invariant seed data. The
resulting CMC slicings of Schwarzschild-de Sitter and Nariai are described.Comment: 33 pages, 25 figure
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