Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
11-1999
Abstract/Description
In [STT], a Hamiltonian system of the form (1. 0)− u+ u= h (t)∇ F (u) was studied, where h is an almost periodic (defined in a moment) function, and F: Rn→ R a “superquadratic” potential. That is, F (q) behaves like q to a power greater than 2, with F (q)/| q| 2→ 0 as| q|→ 0 and F (q)/| q| 2→∞ as| q|→∞. For example, F (q)=| q| p− 1q with p> 1 would qualify. The authors found that (1.0) must have a nonzero solution homoclinic to zero. Since this result, many papers (see [CMN],[R1], and [ACM], for example) have been written concerning Hamiltonian systems with almost periodic terms.
Publication Title
Calculus of Variations and Partial Differential Equations
DOI
https://doi.org/10.1007/s005260050138
Publisher
Springer Nature
Scholarly Commons Citation
Spradlin, G. A singularly perturbed elliptic partial differential equation with an almost periodic term. Calc Var 9, 207–232 (1999). https://doi.org/10.1007/s005260050138
Included in
Ordinary Differential Equations and Applied Dynamics Commons, Partial Differential Equations Commons
Additional Information
Dr. Spradlin was not affiliated with Embry-Riddle Aeronautical University at the time this paper was published.