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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
An Elliptic Partial Differential Equation With A Symmetrical Almost Periodic Term, Gregory S. Spradlin
An Elliptic Partial Differential Equation With A Symmetrical Almost Periodic Term, Gregory S. Spradlin
Publications
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) …
A Singularly Perturbed Elliptic Partial Differential Equation With An Almost Periodic Term, Gregory S. Spradlin
A Singularly Perturbed Elliptic Partial Differential Equation With An Almost Periodic Term, Gregory S. Spradlin
Publications
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 …