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Existence theory for the Hartree equation. (English) Zbl 0287.34032


MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
35Q99 Partial differential equations of mathematical physics and other areas of application
45K05 Integro-partial differential equations
35P05 General topics in linear spectral theory for PDEs
47J05 Equations involving nonlinear operators (general)
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References:

[1] Reeken, M., A general theorem on bifurcation and its application to the Hartree equation of the Helium atom. J. Math. Phys. 11, 2505–2512 (1970).
[2] Stuart, C. A., Some bifurcation theory for k-set contractions. Proc. Lond. Math. Soc. (to appear). · Zbl 0268.47064
[3] Kato, T., Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1966. · Zbl 0148.12601
[4] Titchmarsh, E. C., Eigenfunction Expansions, Part II. London: Oxford Univ. Press 1962. · Zbl 0099.05201
[5] Hellwig, G., Differential Operators of Mathematical Physics. Reading: Addison-Wesley 1967. · Zbl 0163.11801
[6] Dunford, N., & J. Schwartz, Linear Operators, Part II. New York: Interscience 1963. · Zbl 0128.34803
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