Nodal Sets and Morse Indices of Solutions of Super-linear Elliptic PDEs

Journal of Functional Analysis

Volumn 160, Issue 1, 1998, Pages 223-253

  Yang, Xue Feng ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002543924     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1998.3301     Document Type: Article

References (21)

1. Ambrosetti A., Rabinowitz P. H. Dual variational methods in critical point theory and applications. J. Funct. Anal. 14:1973;369-381.
2. Bahri A. Topological results on a certain class of functionals and applications. J. Funct. Anal. 41:1981;397-427.
3. Bahri A., Lions P. L. Solutions of superlinear elliptic equations and their Morse indices. Comm. Pure Appl. Math. XLV:1992;1205-1215.
4. Benci V., Fortunato D. A remark on the nodal regions of the solutions of some superlinear elliptic equations. Proc. Royal Soc. Edinburgh Sect. A. 111:1989;123-128.
5. Chang K. C. Infinite Dimensional Morse Theory and Multiple Solution Problems. PNDLE. 6:1991;Birkhäuser, Basel.
6. Coffman C. V. Lyusternik-Schnirelman theory: complementary principles and the Morse index. Nonlinear Anal. 12:1988;506-529.
7. Courant R., Hilbert D. Methoden der Mathematischen Physik. 1931;Springer-Verlag, Berlin/New York.
8. Donnelly H., Fefferman C. Nodal sets of eigenfunctions on Riemannian manifolds. Invent. Math. 93:1988;161-183.
9. Donnelly H., Fefferman C. Nodal sets of eigenfunctions: Riemannian manifolds with boundary. Analysis, Et Cetera. 1990;Academic Press, San Diego. p. 251-262.
10. Hardt R., Simon L. Nodal sets for solutions of elliptic equations. J. Differential Geom. 30:1989;505-522.
11. Gilbarg D., Trudinger N. S. Elliptic Partial Differential Equations of Second Order. 1977;Springer-Verlag, Berlin/New York.
12. Kreith K. Nodal domain theorems for general elliptic equations. Rocky Mountain J. Math. 1:1971;419-425.
13. Lazer M., Solimini S. Nontrivial solutions of operator equations and Morse indices of critical points of min-max type. Nonlinear Anal. 10:1986;411-413.
14. Lin F. H. A uniqueness theorem for parabolic equations. Comm. Pure Appl. Math. 42:1988;125-136.
15. Jerison D., Kenig C. Unique continuation and absence of positive eigenvalues for Schrödinger operators. Ann. Math. 121:1985;463-494.
16. Pohozaev S. I. Eigenfunctions ofΔuλfu. Soviet Math. Dokl. 6:1965;1408-1411.
17. Rabinowitz P. H. Dual variational methods for nonlinear eigenvalue problems. Eigenvalues of Nonlinear Problems. 1974;CIME Varenna. p. 140-195.
18. Solimini S. Morse index estimates in mini-max theories. Manuscripta Math. 63:1989;421-453.
19. Viterbo C. Indice de Morse des points critiques obtenus par minimax. Ann. Inst. H. Poincaré Anal. Non Linéaire. 5:1988;221-226.
20. Yang X. F. The Morse critical groups and the min-max theorem. Chinese Ann. Math. Ser. B. 12:1991;202-206.
21. Yau S. T. Problem section. Seminar on Differential Geometry. 1982;Princeton Univ. Press, Princeton.