Bifurcation from infinity for asymptotically linear elliptic eigenvalue problems. (English) Zbl 1219.35165

Summary: We are going to discuss bifurcation from infinity for asymptotically linear elliptic eigenvalue problems having nonlinear boundary conditions. Behavior of the bifurcation components is also studied.


35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35B32 Bifurcations in context of PDEs
47J15 Abstract bifurcation theory involving nonlinear operators
Full Text: DOI


[1] Adams, R. A., Sobolev Spaces (1975), Academic Press: Academic Press San Diego · Zbl 0186.19101
[2] Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18, 620-709 (1976) · Zbl 0345.47044
[3] Amann, H., Nonlinear elliptic equations with nonlinear boundary conditions, (Eckhaus, W., New Developments in Differential Equations. New Developments in Differential Equations, Math. Studies, 21 (1976), North-Holland: North-Holland Amsterdam), 43-63
[4] Ambrosetti, A.; Arcoya, D.; Buffoni, B., Positive solutions for some semi-positone problems via bifurcation theory, Differential Integral Equations, 7, 655-663 (1994) · Zbl 0808.35030
[5] Ambrosetti, A.; Hess, P., Positive solutions of asymptotically linear elliptic eigenvalue problems, J. Math. Anal. Appl., 73, 411-422 (1980) · Zbl 0433.35026
[6] Gilbarg, D.; Trudinger, N. S., Elliptic Partial Differential Equations of Second Order (1983), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0691.35001
[7] Krasnosel’skii, M. A., Positive Solutions of Operator Equations (1964), Noordhoff · Zbl 0121.10604
[8] Rabinowitz, P. H., Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7, 487-513 (1971) · Zbl 0212.16504
[9] Umezu, K., Global positive solution branches of positone problems with nonlinear boundary conditions, Differential Integral Equations, 13, 669-686 (2000) · Zbl 0983.35051
[10] Wiebers, H., Critical behavior of nonlinear elliptic boundary value problems suggested by exothermic reactions, Proc. Roy. Soc. Edinburgh Sect. A, 102, 19-36 (1986) · Zbl 0609.35073
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.