Multiple Bound States of Nonlinear Schrödinger Systems
- First Online:
This paper is concerned with existence of bound states for Schrödinger systems which have appeared as several models from mathematical physics. We establish multiplicity results of bound states for both small and large interactions. This is done by different approaches depending upon the sizes of the interaction parameters in the systems. For small interactions we give a new approach to deal with multiple bound states. The novelty of our approach lies in establishing a certain type of invariant sets of the associated gradient flows. For large interactions we use a minimax procedure to distinguish solutions by analyzing their Morse indices.
Unable to display preview. Download preview PDF.
- 9.Chang K.C.: Infinite Dimensional Morse Theory and Multiple Solution Problems, Progress in Nonlinear Differential Equations and Their Applications, 6. Birkhäuser, Boston (1993)Google Scholar
- 11.Dancer, E.N., Wei, J.C., Weth, T.: A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system. PreprintGoogle Scholar
- 12.Deimling K.: Ordinary Differential Equations in Banach Spaces, Lecture Notes in Mathematics, vol. 596. Springer-Verlag, Berlin (1977)Google Scholar
- 14.Genkin, G.M.: Modification of superfluidity in a resonantly strongly driven Bose-Einstein condensate. Phys. Rev. A, 65 (2002), No.035604Google Scholar
- 17.Kanna, T., Lakshmanan, M.: Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations. Phys. Rev. Lett., 86, 5043(1–4) (2001)Google Scholar
- 22.Montefusco, E., Pellacci, B., Squassina, M.: Semiclassical states for weakly coupled nonlinear Schrödinger systems. PreprintGoogle Scholar
- 25.Rabinowitz, P.H.: Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Reg. Conf. Ser. Math. 65, Providence, R.I.: Amer. Math. Soc., 1986Google Scholar
- 29.Wei, J.C., Weth, T.: Radial solutions and phase seperation in a system of two coupled Schrödinger equations. Arch. Rational Mech. Anal., On-line First, doi:10:1007/s00205-008-0121-9, 2008