Nonlinear schrödinger equations with steep potential well

Communications in Contemporary Mathematics

Volumn 3, Issue 4, 2001, Pages 549-569

  Bartsch, Thomas ^a   Pankov, Alexander ^b   Wang, Zhi Qiang ^c  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b VINNYTSIA MYKHAILO KOTSIUBYNSKYI STATE PEDAGOGICAL UNIVERSITY   (Ukraine)

^c UTAH STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346289757     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199701000494     Document Type: Article

References (26)

1. T. Bagby, Quasitopologies and rational approximation, J. Funct. Anal. 10 (1972) 259-268.
2. T. Bartsch, Infinitely many solutions of a symmetric Dirichlet problem, Nonlin. Anal.: Theory, Meth. and Appl. 20 (1993) 1205-1216.
3. T. Bartsch, Critical point theory on partially ordered Hubert spaces, to appear in J. Funct. Anal.
4. n, Comm. Partial Differential Equations 20 (1995) 1725-1741.
5. T. Bartsch and Z.-Q. Wang, Sign changing solutions of nonlinear Schrödinger equations, Top. Meth. Nonlin. Anal. 13 (1999) 191-198.
6. F. A. Berezin and M. A. Shubin, The Schrödinger Equation, Dordrecht, Kluwer (1991).
7. A. Floer and A. Weinstein, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal. 69 (1986) 397-408.
8. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order Springer (1983).
9. C. Gui, Multi-peak solutions for a semilinear Neumann problem, Duke Math. J. 84 (1996) 739-769.
10. L. I. Hedberg, Non-linear potentials and approximation in the mean by analytic functions, Math. Z. 129 (1972) 299-319.
11. P. D. Hislop and I. M. Sigal, Introduction to Spectral Theory. With Applications to Schrödinger Operators, Springer (1996).
12. V. Kondrat'ev and M. Shubin, Discreteness of spectrum for the Schrödinger operators on manifolds of bounded geometry, Operator theory: Advances and Applications 110 (1999) 185-226.
13. Y. Y. Li, On a singularly perturbed elliptic equation, Adv. in Differential Equations 2 (1997) 955-980.
14. P. Lions, The concentration-compactness principle in the calculus of variations: The locally compact case, Part I, Ann. Inst. H. Poincaré, Anal. Non Linéaire 1 (1984) 109-145.
15. V. G. Maz'ya, Sobolev Spaces, Springer (1985).
16. A. M. Molchanov, On the discreteness of the spectrum conditions for self-adjoint differential equations of the second order, Trudy Mosk. Matem. Obshchestva 2 (1953) 169-199 (in Russian).
17. A. Persson, Bounds for the discrete part of the spectrum of a semi-bounded Schrödinger operator, Math. Scand. 8 (1960) 143-153.
18. M. del Pino and P. Felmer, Multi-peak bound states for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré, Anal. Non Linéaire 15 (1998) 127-149.
19. J. C. Polking, A Leibniz formula for some differentiation operators of fractional order, Indiana Univ. Math. J. 21 (1972) 1019-1029.
20. P. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43 (1992) 270-291.
21. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. IV. Academic Press (1978).
22. B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S.) 7 (1982) 447-526.
23. N, Calc. Var. 11 (2000) 119-142.
24. X. Wang, On concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys. 153 (1993) 229-244.
25. Z.-Q. Wang, Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations, J. Differential Equations 159 (1999) 102-137.
26. M. Willem, Minimax Theorems, Boston, Birkhäuser (1996).