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Positive solutions of asymptotically linear elliptic eigenvalue problems. (English) Zbl 0433.35026

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
55M25 Degree, winding number
35B32 Bifurcations in context of PDEs
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[1] Amann, H, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM rev., 18, 620-709, (1976) · Zbl 0345.47044
[2] Amann, H, Nonlinear eigenvalue problems having precisely two solutions, Math. Z., 150, 27-37, (1976) · Zbl 0329.35027
[3] Amann, H; Laetsch, T, Positive solutions of convex nonlinear eigenvalue problems, Indiana univ. math. J., 25, 259-270, (1976) · Zbl 0329.35028
[4] {\scA. Ambrosetti}, On the exact number of positive solutions of convex nonlinear problems, Boll. Un. Mat. Ital., in press. · Zbl 0391.35031
[5] Brown, K.J; Budin, H, Multiple positive solutions for a class of nonlinear boundary value problems, J. math. anal. appl., 60, 329-338, (1977) · Zbl 0361.35023
[6] Hess, P, Multiple solutions of asymptotically linear elliptic boundary value problems, (), in press · Zbl 0421.35024
[7] Keener, J.P; Keller, H.B, Positive solutions of convex nonlinear eigenvalue problems, J. differential equations, 16, 103-125, (1974) · Zbl 0287.35074
[8] Rabinowitz, P.H, Some global results for nonlinear eigenvalue problems, J. functional analysis, 7, 487-513, (1971) · Zbl 0212.16504
[9] Rabinowitz, P.H, Théorie du degré topologique et applications à des problèmes aux limites non linéaires, Notes univ. Paris VI et CNRS, (1975), (rédigés par H. Berestycki)
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