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Remarks on Bifurcation from the Essential Spectrum

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Topics in Nonlinear Analysis

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 35))

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Abstract

In this note we prove the existence of two families of solutions bifurcating from the essential spectrum for problem (1) below. We use a new perturbation method recently developed (see [1], [2], [3]).

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References

  1. A. Ambrosetti — M. Badiale, “Homoclinics: Poincaré-Melnikov type results via a variational approach”, Annales I.H.P. — Analyse nonlin. 15 (1998), 233–252.

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  2. A. Ambrosetti — M. Badiale, “Variational perturbative methods and bifurcation of bound states from the essential spectrum”, Proc. Royal Soc. Edinburgh, to appear.

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  3. A. Ambrosetti — M. Badiale — S. Cingolani, “Semiclassical states of nonlinear Schrö-dinger equations”, Archive Rat. Mech. Anal. 140 (1997), 285–300.

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  4. R.J. Magnus, “On perturbation of translationally invariant differential equations”, Proc. Royal Soc. Edinburgh 110-A (1988), 1–25.

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  5. C. Stuart, “Bifurcation from the essential spectrum”, Topological Nonlinear Analysis, II. M. Matzeu, A. Vignoli eds., PNDLE 27, Birkhäuser 1997, 397–444.

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  6. C. Stuart, “Bifurcation of homoclinic orbits and bifurcation from the essential spectrum”, SIAM J. Math. Anal. 20 (1989), 1145–1171.

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© 1999 Springer Basel AG

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Ambrosetti, A., Badiale, M. (1999). Remarks on Bifurcation from the Essential Spectrum. In: Escher, J., Simonett, G. (eds) Topics in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 35. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8765-6_1

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  • DOI: https://doi.org/10.1007/978-3-0348-8765-6_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9764-8

  • Online ISBN: 978-3-0348-8765-6

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