17,224 research outputs found
Nonzero solutions of perturbed Hammerstein integral equations with deviated arguments and applications
We provide a theory to establish the existence of nonzero solutions of
perturbed Hammerstein integral equations with deviated arguments, being our
main ingredient the theory of fixed point index. Our approach is fairly general
and covers a variety of cases. We apply our results to a periodic boundary
value problem with reflections and to a thermostat problem. In the case of
reflections we also discuss the optimality of some constants that occur in our
theory. Some examples are presented to illustrate the theory.Comment: 3 figures, 23 page
Bifurcation of periodic solutions to the singular Yamabe problem on spheres
We obtain uncountably many periodic solutions to the singular Yamabe problem
on a round sphere, that blow up along a great circle. These are (complete)
constant scalar curvature metrics on the complement of inside ,
, that are conformal to the round (incomplete) metric and "periodic"
in the sense of being invariant under a discrete group of conformal
transformations. These solutions come from bifurcating branches of constant
scalar curvature metrics on compact quotients of .Comment: LaTeX2e, 12 pages, final version. To appear in J. Differential Geo
- β¦