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Bifurcation for variational problems when the linearisation has no eigenvalues. (English) Zbl 0458.47048


MSC:

47J05 Equations involving nonlinear operators (general)
35B32 Bifurcations in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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[1] Stuart, C.A, Three fundamental theorems on bifurcation, () · Zbl 0446.58005
[2] Nehari, Z, On a non-linear differential equation arising in nuclear physics, () · Zbl 0208.35302
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[4] Sansone, G, Su un’equazione differenziale non lineare Della fisica nucleare, () · Zbl 0249.34038
[5] Berger, M.S, On the existence and structure of stationary states for a non-linear klien-gordkn equation, J. functional analysis, 9, 249-261, (1972)
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[10] Lyusternik, L.A; Sobolev, V.J, Elements of functional analysis, (1974), Halsted New Dehli · Zbl 0096.07802
[11] Hartman, P, Ordinary differential equations, (1973), Baltimore · Zbl 0125.32102
[12] Stuart, C.A, An example in non-linear functional analysis, the Hartree equation, J. math. anal. appl., 49, 725-733, (1975) · Zbl 0311.47032
[13] Stuart, C.A, Bifurcation pour des problèmes de Dirichlet et de Neumann sans valeurs propres, C. R. acad. sci. Paris, 288, 761-764, (1979) · Zbl 0397.34079
[14] {\scC. A. Stuart}, Bifurcation for Dirichlet problems without eigenvalues, Proc. London Math. Soc., in press. · Zbl 0505.35010
[15] Stuart, C.A, Bifurcation for Neumann problems without eigenvalues, J. differential equations, 36, 391-407, (1980) · Zbl 0468.34009
[16] Stuart, C.A, A variational method for bifurcation problems when the linearisation has no eigenvalues, Atti del SAFA III, Bari, 154-180, (1978) · Zbl 0432.47037
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