Summary
We consider the nonlinear Dirichlet boundary value problems for the second order equation
the fourth order equation
with p≧2, a ε C1, c ε C, a, c>0, g Carathéodory's function, and the partial differential equation
on ∂Ω, with p>1, Ω⊂RN, bounded domain. There is proved a global bifurcation result of Rabinowitz's type using the degree theoretical approach for the mappings acting from the Banach space X into its dual X*.
Article PDF
Similar content being viewed by others
References
H. Amann,A note on the degree theory for gradient mappings, Proc. Amer. Math. Society,85 (1982), pp. 591–595.
A. Anane,Simplicité et isolation de la premier valeur propre du p-laplacian avec poids, C. R. Acad. Sci. Paris,305, Sér. 1 (1987), pp. 725–728.
F. E. Browder -W. F. Petryshyn,Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces, J. Functional Analysis,3 (1969), pp. 217–245.
E. N. Dancer,On the structure of the solutions of non-linear eigenvalue problems, Indiana Univ. Math. J.,23 (11) (1974), pp. 1069–1076.
P. Drábek,Ranges of α-homogeneous operators and their perturbations, Čas. Pěst. Mat.,105 (1980), pp. 167–183.
S. Fučík -J. Nečas -J. Souček -V. Souček,Spectral Analysis of Nonlinear Operators, Lecture Notes in Math.,346, Springer, Berlin, 1973.
A. Kratochvíl -J. Nečas,On the discretness of the spectrum of nonlinear forth-order Sturm-Liouville problem (in Russian), Comment. Math. Univ. Carolinae,12 (1971), pp. 639–653.
L.Libourty,Traité de Glaceologie, Masson and Lie, Paris (I) 1964 et (II) 1965.
J. Nečas,On the discretness of the spectrum of nonlinear second-order Sturm-Liouville problem (in Russian), Dokl. Akad. Nauk SSSR,201 (5) (1971), pp. 1045–1048.
M. C. Péllisier -L. Reynaud,Étude d'un modèle mathématique d'écoulement de glacier, C. R. Acad. Sci. Paris, Sér. A,279 (1979), pp. 531–534.
R. H. Rabinowitz,Some global results for nonlinear eigenvalue problem, J. Functional Analysis,7 (1971), pp. 487–513.
I. V. Skrypnik,Nonlinear Elliptic Equations of Higher Order (in Russian), Naukovaja Dumka, Kyjev, 1973.
P. Tolksdorf,Regularity of a more general class of quasi-linear elliptic equations, J. Differential Equations,51 (1984), pp. 126–150.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Drábek, P. On the global bifurcation for a class of degenerate equations. Annali di Matematica pura ed applicata 159, 1–16 (1991). https://doi.org/10.1007/BF01766290
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01766290