Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity
| dc.contributor.author | Spradlin, Gregory S. | |
| dc.date.accessioned | 2021-04-05T20:25:43Z | |
| dc.date.available | 2021-04-05T20:25:43Z | |
| dc.date.issued | 2004-02-12 | |
| dc.description.abstract | 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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Spradlin, G. S. (2004). Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity. <i>Electronic Journal of Differential Equations, 2004</i>(21), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13340 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Mountain Pass Theorem | |
| dc.subject | Variational methods | |
| dc.subject | Nehari manifold | |
| dc.subject | Homoclinic solutions | |
| dc.title | Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity | |
| dc.type | Article |