Hamiltonian constants for several new entire solutions

Abstract

Using the Hamiltonian identities and the corresponding Hamiltonian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.

Keywords

Hamiltonian identity / Young’s law / Schrodinger equation / Allen-Cahn equation / period solution / contact angle

References

[1] Dancer N. New solutions of equations on ℝⁿ. Annali Della Scuola Normale Superiore Di Pisa, 2001, 30: 535-563.

[2] Gui C. Hamiltonian identity for elliptic partial differential equations. Journal of Functional Analysis, 2008, 254: 904-933.

[3] Malchiodi A. Some new entire solutions of semilinear elliptic equations on ℝⁿ. Preprint, 2007

[4] Young T. An essay on the cohension of fluids. Philos Trans Roy Soc London, 1805, 95: 65-87.