Submitting Campus

Daytona Beach

Department

Department of Mathematics

Document Type

Article

Publication/Presentation Date

2-2004

Abstract/Description

We study a Hamiltonian system that has a superquadratic potential and is asymptotic to an autonomous system. In particular, we show the existence of a nontrivial solution homoclinic to zero. Many results of this type rely on a convexity condition on the nonlinearity, which makes the problem resemble in some sense the special case of homogeneous (power) nonlinearity. This paper replaces that condition with a different condition, which is automatically satisfied when the autonomous system is radially symmetric. Our proof employs variational and mountain-pass arguments. In some similar results requiring the convexity condition, solutions inhabit a submanifold homeomorphic to the unit sphere in the appropriate Hilbert space of functions. An important part of the proof here is the construction of a similar manifold, using only the mountain-pass geometry of the energy functional.

Publication Title

Electronic Journal of Differential Equations

Publisher

Texas State University, San Marcos, Department of Mathematics

Included in

Mathematics Commons

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