On principal eigenvalues for quasilinear elliptic differential operators: An Orlicz-Sobolev space setting

Nonlinear Differential Equations and Applications

Volumn 6, Issue 2, 1999, Pages 207-225

  Garcia Huidobro M ^a   Le, V K ^b   Manasevich R ^c   Schmitt, K ^d  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

^c UNIVERSITY OF CHILE   (Chile)

^d UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001594399     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000300050073     Document Type: Article

References (26)

1. R. ADAMS, Sobolev Spaces, Acad. Press, New York, 1975.
2. H. AMANN, Liusternik-Schnirelman theory and non-linear eigenvalue problems, Math. Ann. 199, 55-72 (1972).
3. A. ANANE, Simplicité et isolation de la première valeur propre du pLaplacien, C. R. Acad. Sci Paris 305, 725-728 (1987).
4. C. COFFMANN, Lyusternik-Schnirelman theory and eigenvalue problems for monotone potential operators, J. Fund. Anal. 14, 237-252 (1973).
5. T. DONALDSON, Nonlinear elliptic boundary value problems in OrliczSobolev spaces, J. Diff. Equations 10, 507-528 (1971).
6. I. EKELAND, R. TEMAM, Convex Analysis and Variational Problems, North Holland, American Elsevier, New York, 1976.
7. L. FRIEDLANDER, Asymptotic behavior of the eigenvalues of the pLaplacian, Comm. Part. Diff. Equations 14, 1059-1069 (1989).
8. J. GARCÍA AZORERO, I. PERAL ALONSO, Existence and nonuniqueness for the p-Laplacian: Nonlinear eigenvalues, Comm. Part. Diff. Equations 12, 1389-1430 (1987).
9. J. GARCÍA AZORERO, I. PERAL ALONSO, Comportement asymptotique des valeurs propres du p-laplacien, C.R. Acad. Sci. Paris 307, 75-78 (1988).
10. M. GARCÍA-HUIDOBRO, R. MANÁSEVICH, K. SCHMITT, On the principal eigenvalue of p-Laplacian like operators, J. Diff. Equations 130, 235-246 (1966).
11. M. GARCÍA-HUIDOBRO, R. MANÁSEVICH, F. ZANOLIN, A Fredholmlike result for strongly nonlinear second order ODE's, J. Diff. Equations 114, 132-167 (1994).
12. J. GOSSEZ, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients
13. J. GOSSEZ, A strongly nonlinear elliptic problem in Orlicz-Sobolev spaces, Proc. Symp. Pure Mathematics 45, 455-462 (1986).
14. M. KRASNOSELS'KII, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, 1963.
15. M. KRASNOSELS'KII, J. RUTIC'KII, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
16. [IG] R. S. KUBRUSLY, Variational methods for nonlinear eigenvalue inequalities, Diff. Integral Equations 3, 923-952 (1990).
17. A. KUFNER, O. JOHN, S. FUCIK, Function Spaces, Noordhoff, Leyden, 1977.
18. V. LE, K. SCHMITT, Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems, vol. 123, Appl. Math. Sciences, Springer, New York, 1997.
19. p-2u=0, Proc. A.M.S. 109, 157-164 (1990).
20. K. NAKURAWA, T. SUZUKI, Nonlinear eigenvalue problem for a modified capillary surface equation, Funk. Ekvac. 37, 81-100 (1994).
21. M. ÔTANI, Existence and nonexistence,of nontrivial solutions of some nonlinear degenerate elliptic equations, J. Funct. Anal. 76, 140-159 (1988).
22. M. N. RAO, Z. D. REN, Theory of Orlicz Spaces, Marcel Dekker, New York, 1985.
23. V. L. SHAPIRO, Quasilinear ellipticity and the 1st eigenvalue, Comm. Part. Diff. Equations 16, 1819-1855 (1991).
24. M. STRUWE, Variational Methods, Springer-Verlag, New York, 1990.
25. 1-manifolds, Ann. Inst. Henri Poincaré5, 119-139 (1988).
26. E. ZEIDLER, Nonlinear Functional Analysis and its Applications, Vol.11: Variational Methods, Springer, Berlin, 1986.