Variational eigenvalues of degenerate eigenvalue problems for the weighted p-laplacian

Advanced Nonlinear Studies

Volumn 5, Issue 4, 2005, Pages 573-585

  Lê, An ^a   Schmitt, Klaus ^b  

^a MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

Eigenvalue problems; P Laplacian; Weighted Sobolev spaces

Indexed keywords

EID: 29144466663     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2005-0406     Document Type: Article

References (20)

1. A. Anane, Simplicité et isolation de la première valeur propre du p-laplacien avec poids, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), 725-728.
2. A. Anane and N. Tsouli, On the second eigenvalue of the p-Laplacian, in Nonlinear Partial Differential Equations (Fès, 1994), vol. 343 of Pitman Res. Notes Math. Ser., Longman, Harlow, 1996, pp. 1-9.
3. M. Arias, J. Campos, M. Cuesta, and J.-P. Gossez, Sur certains problèmes elliptiques asymétriques avec poids indéfinis, C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), 215-218.
4. F. Browder, Existence theorems for nonlinear partial differential equations, in Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 1-60.
5. M. Cuesta, Eigenvalue problems for the p-Laplacian with indefinite weights, Electron. J. Differential Equations 2001 (2001), No. 33 (electronic).
6. 1 manifolds via Ekeland variational principle, Abstr. Appl. Anal. 2003 (2003), 757-768.
7. P. Drábek, A. Kufner, and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, vol. 5 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter & Co., Berlin, 1997.
8. P. Drábek and S. B. Robinson, Resonance problems for the p-Laplacian, J. Funct. Anal. 169(1999), 189-200.
9. _, Eigenvalue problems, resonance problems and open problems, in Variational methods: open problems, recent progress, and numerical algorithms, vol. 357 of Contemp. Math., Amer. Math. Soc., Providence, RI, 2004, pp. 141-149.
10. J. P. García Azorero and I. Peral Alonso, Existence and nonuniqueness for the p-Laplacian: nonlinear eigenvalues, Comm. Partial Differential Equations 12 (1987), 1389-1430.
11. J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, New York, 1993.
12. A. Le, Eigenvalue problems for the p-Laplacian, to appear in Nonlinear Analysis, TMA, (2005).
13. V. Le and K.Schmitt, On boundary value problems for degenerate quasilinear elliptic equations and inequalities, J. Differential Equations 144 (1998), 170-218.
14. V. K. Le and K. Schmitt, Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems, Springer-Verlag, New York, 1997.
15. p-2u = 0" [Proc. Amer. Math. Soc. 109 (1990), 157-164],
16. Proc. Amer.Math. Soc., 116(1992),583-584.
17. 1 manifolds, Ann. Inst. Henri Poincaré 5(1988), 119-139.
18. K. Yosida, Functional Analysis, 6th ed., Springer, New York, 1995.
19. E. Zeidler, The Ljusternik-Schnirelman theory for indefinite and not necessarily odd nonlinear operators and its applications, Nonlinear Anal. 4 (1980), 451-489.
20. _, Nonlinear Functional Analysis and its Applications, Vol. 3: Variational Methods and Optimization, Springer, Berlin, 1985.