Multiple positive solutions for a nonlinear Schrödinger equation

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 51, Issue 3, 2000, Pages 366-384

  Bartsch, Thomas ^a   Wang, Zhi Qiang ^b  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b UTAH STATE UNIVERSITY   (United States)

Author keywords

Localized solutions; Nonlinear schr dinger equation; Potential well; Singular limit

Indexed keywords

EID: 0034342136     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/pl00001511     Document Type: Article

References (23)

1. Adimurthi, Mancini, G., and Yadava, S.: The role of the mean curvature in semilinear Neumann problem involving critical exponent. Comm. Partial Differential Equations 20 (1995), 591-631.
2. Ambrosetti, A., Badiale, M., and Cingolani, S.: Semiclassical states of nonlinear Schrödinger equations. Arch. Rational Mech. Anal. 140 (1997), 285-300.
3. Bahri, A. and Coron, J. M.: On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain. Comm. Pure Appl. Math. 41 (1988), 253-294.
4. n. Comm. Partial Differential Equations 20 (1995), 1725-1741.
5. Benci, V. and Cerami, G.: The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems. Arch. Rational Mech. Anal. 114 (1991), 79-83.
6. Brézis, H. and Nirenberg, L.: Positive solutions of nonlinear elliptic equations involving critical Sobolev exponenets. Comm. Pure Appl. Math. 36 (1983), 437-447.
7. del Pino, M. and Felmer, P.: Local mountain passes for semilinear elliptic problems in unbounded domains. Calc. Variations and Part. Diff. Eq. 4 (1996), 121-137.
8. del Pino, M. and Felmer, P.: Multi-peak bound states for nonlinear Schrödinger equations. Ann. Inst. H. Poincaré. Anal. Non Linéaire 15 (1998), 127-149.
9. Floer, A. and Weinstein, A.: Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. J. Funct. Anal. 9 (1986), 397-408.
10. Gui, C.: Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method. Comm. Partial Differential Equations 21 (1996), 787-820.
11. Li, Y. Y.: On a singularly perturbed elliptic equation. Adv. Diff. Equ. 2 (1997), 955-980.
12. Lions, P.: 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.
13. N. Top. Meth. Nonlin. Anal. 7 (1996), 171-185.
14. Ni, W. and Takagi, I.: On the shape of least energy solutions to a semilinear Neumann problem. Comm. Pure Appl. Math. 45 (1991), 819-851.
15. a). Comm. Partial Differential Equations 13 (1988), 1499-1519.
16. a)". Comm. Partial Differential Equations 14 (1989), 833-834.
17. Oh, Y.: On positive multi-bump bound states of nonlinear Schrödinger equations. Comm. Math. Phys. 131 (1990), 223-253.
18. Rabinowitz, P.: On a class of nonlinear Schrödinger equations. Z. Angew. Math. Phys. 43 (1992), 270-291.
19. Rey, O.: The role of Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent. J. Funct. Anal. 89 (1990), 1-52.
20. Rey, O.: Contraction of solutions to elliptic equations with critical nonlinearity. Ann. Inst. H. Poincaré. Anal. Non Linéaire 9 (1992), 201-218.
21. Wang, Z.-Q.: On concentration of positive bound states of nonlinear Schrödinger equations. Comm. Math. Phys. 153 (1993), 229-244.
22. Wang, Z.-Q.: On the existence of multiple, single-peaked solutions for a semilinear Neumann problem. Arch. Rational Mech. Anal. 120 (1992), 375-399.
23. Wang, Z.-Q.: The effect of the domain geometry on the number of positive solutions of Neumann problems with critical exponents. Diff. Int. Equations 8 (1995), 1533-1554.