Critical Phenomena in Linear Elliptic Problems

Journal of Functional Analysis

Volumn 154, Issue 1, 1998, Pages 42-66

  Tertikas, Achilles ^a  

^a UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001887720     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1997.3199     Document Type: Article

References (42)

1. Aizenman M., Simon B. Brownian motion and Harnack inequality for Schrödinger operators. Comm. Pure Appl. Math. XXXV:1982;209-273.
2. Agmon S. Bounds on exponential decay of eigenfunctions of Schrödinger operators. Schrödinger Operators. Lecture Notes in Math. 1159:1985;Springer-Verlag, Berlin/New York. p. 1-38.
3. Agmon S. Spectral theory of Schrödinger operators on Euclidean and on Non-Euclidean spaces. Comm. Pure Appl. Math. XXXIX:1986;S3-S16.
4. N. Proc. Amer. Math. Soc. 116:1992;701-706.
5. Aubin T. Équations différentielles nonlinéaires et problème de Yamabe concernant la courbure scalaire. J. Math. Pures Appl. (9). 55:1976;269-296.
6. Barhi A., Coron J. M. On the nonlinear elliptic equation involving the critical Sobolev exponent: The effect of the topology of the domain. Comm. Pure Appl. Math. XLI:1988;253-294.
7. N. J. Funct. Anal. 88:1990;90-117.
8. Bennett C., Sharpley R. Interpolation of Operators. Pure and Applied Maths. 1988;Academic Press, San Diego.
9. Birman M. S., Solomyak M. Z. Schrödinger operator. Estimates for number of bound states as function-theoretical problem. Amer. Math. Soc. Trans. 2. 150:1992;1-54.
10. Brezis H. Elliptic equations with limiting Sobolev exponents-The impact of topology. Comm. Pure Appl. Math. XXXIX:1986;S17-S39.
11. Brezis H., Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure. Appl. Math. XXXVI:1983;437-477.
12. N. Proc. Am. Math. Soc. 109:1990;147-155.
13. Chang S. Y. A., Wilson J. M., Wolff T. H. Some weighted norm inequalities concerning the Schrödinger operator. Comment. Math. Helv. 60:1985;217-246.
14. Nand related topics. J. Differential Equations. 121:1995;293-313.
15. pnorms of non-critical Schrödinger semigroups. J. Funct. Anal. 102:1991;95-115.
16. Escobar J. F. Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary. Ann. of Math. 136:1992;1-50.
17. Fabes E. B., Garofalo N., Lin F.-H. A partial answer to a conjecture of B. Simon concerning unique continuation. J. Funct. Anal. 88:1990;194-210.
18. Fefferman C. L. The uncertainty principle. Bull. Am. Math. Soc. 9:1983;129-206.
19. 2. Comm. Pure Appl. Math. XLVIII:1995;639-655.
20. Flucher M. Extremal functions for the Trudinger-Moser inequality in 2 dimensions. Comment. Math. Helv. 67:1992;471-497.
21. Gilbarg D., Trudinger N. Elliptic Partial Differential Equations of Second Order. 1983;Springer-Verlag, Berlin/New York.
22. N. Comm. Pure Appl. Math. XLV:1992;1153-1181.
23. Jin Z. Principal eigenvalues with indefinite weight functions. Trans. Am. Math. Soc. 349:1997;1945-1959.
24. Küpper T., Tertikas A. A global branch of positive solutions above the continuous spectrum for problems with indefinite nonlinearities. Proc. Roy. Soc. Edinburgh. 126A:1996;465-482.
25. Lieb E. Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Ann. of Math. 118:1983;349-374.
26. Lions P. L. The concentration - compactness principle in the calculus of variations. The locally compact case, Parts I and II. Ann. Inst. H. Poincaré Sect. A (N.S.). 1:1984;109-145.
27. Lions P. L. The concentration-compactness principle in the calculus of variations. The limit case, Parts I and II. Pev. Mat. Ibero. 1:1985;145-201.
28. Maz'ja V. G. Sobolev Spaces. 1985;Springer-Verlag, Berlin/New York.
29. N. Duke Math. J. 53:1986;869-943.
30. Nagylaki T. Conditions for the existence of clines. Genetics. 80:1975;595-615.
31. Nagylaki T. The diffusion model for migration and selection in a dioecious population. J. Math. Biol. 34:1996;334-360.
32. Nussbaum R. D., Pinchover Y. On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications. J. D'Analyse Math. 59:1992;161-177.
33. Pinchover Y. Criticality and ground states for second-order elliptic equations. J. Differential Equations. 80:1989;237-250.
34. Pinchover Y. On positive Liouville theorems and asymptotic behaviour of solutions of Fuschian type elliptic operator. Ann. Inst. H. Poincaré 11:1994;313-341.
35. Pohozaev S. Eigenfunctions of the equationΔuλfu. Soviet. Math. Dokl. 6:1965;1408-1411.
36. Rellich F. Darstellung der eigenwerte vonΔuλu. Math. Zeit. 46:1940;635-636.
37. G. Rozenblioum, M. Solomyak, On Principal Eigenvalues for Indefinite Problems in the Euclidean Space, 1995.
38. Sawyer E., Wheeden R. L. Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces. Amer. J. Math. 114:1992;813-874.
39. Schechter M. The spectrum of the Schrödinger operator. Trans. Am. Math. Soc. 312:1989;115-128.
40. Simon B. Schrödinger semigroups. Bull. Amer. Math. Soc. (N.S). 7:1982;447-525.
41. Slatkin M. Gene flow and selection in a cline. Genetics. 75:1973;733-756.
42. A. Tertikas, On Continuous Bifurcation.