Existence of Solutions for a Wave Equation with Non-monotone Nonlinearity and a Small Parameter

Authors

Jose F. Caicedo, Universidad Nacional de Colombia
Alfonso Castro, Harvey Mudd CollegeFollow
Rodrigo Duque, Universidad Nacional de Colombia

Document Type

Article - postprint

Department

Mathematics (HMC)

Publication Date

6-2011

Abstract

We provide sufficient conditions for the existence of solutions to a semilinear wave equation with non-monotone nonlinearity involving a small parameter. Our results are based on the analysis of a an operator that characterizes the projection onto the kernel of the wave operator subject to periodic-Dirichlet boundary conditions. Such a kernel is infinite dimensional which makes standard compactness arguments inapplicable.

Comments

Author's post-print manuscript available for download.

For the publisher's PDF, please visit http://dx.doi.org/10.1007/s00032-011-0154-7

Rights Information

© 2011 Springer Verlag

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1007/s00032-011-0154-7

Recommended Citation

Caicedo, Jose F., Alfonso Castro and Rodrigo Duque. "Existence of Solutions for a Wave Equation with Non-monotone Nonlinearity and a Small Parameter", Milan Journal of Mathematics, Volume 79, Number 1, (2011), pp. 207-220.