Abstract
We consider elliptic equations on RN+1 of the form Δxu+uyy+g(x,u)=0,(x,y)∈RN×R where g(x,u) is a sufficiently regular function with g(⋅,0)≡0. We give sufficient conditions for the existence of solutions of (1) which are quasiperiodic in y and decaying as |x|→∞ uniformly in y. Such solutions are found using a center manifold reduction and results from the KAM theory. We discuss several classes of nonlinearities g to which our results apply.
Original language | English (US) |
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Pages (from-to) | 6109-6164 |
Number of pages | 56 |
Journal | Journal of Differential Equations |
Volume | 262 |
Issue number | 12 |
DOIs | |
State | Published - Jun 15 2017 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier Inc.
Keywords
- Center manifold
- Elliptic equations
- Entire solutions
- KAM theorem
- Nemytskii operators on Sobolev spaces
- Quasiperiodic solutions