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Asymptotically Critical Points and Multiple Solutions in the Elastic Bounce Problem

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Variational Analysis and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 79))

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References

  1. T. Bartsch and M. Clapp. Critical point theory for indefinite functionals with symmetries. J. Funct. Anal., 138(1): 107–136, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  2. V. Benci and F. Giannoni. Periodic bounce trajectories with a low number of bounce points. Ann. Inst. H. Poincaré, 6(l):73–93, 1989.

    MATH  MathSciNet  Google Scholar 

  3. G. Buttazzo and D. Percivale. On the approximation of the elastic bounc problem on riemanian manifolds. J. Diff. Eq., 47:227–245, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Carriero, A. Leaci, and E. Pascali. Convergenza per l’equazione degli integrali primi associati al problema del rimbalzo unidimensionale. Ann. Mat. Pura Appl., 133:227–256, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Chobanov, A. Marino, and D. Scolozzi. Evolution equation for the eigenvalue problem for the laplace operator with respect to an obstacle. Rend. Accad. Naz. Sci. XL Mem. Mat., 14(5):139–162, 1990.

    MATH  MathSciNet  Google Scholar 

  6. G. Chobanov, A. Marino, and D. Scolozzi. Multiplicity of eigenvalues for the laplace operator with respect to an obstacle, and nontangency conditions. Nonlinear Anal., 15(3): 199–215, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Degiovanni. Multiplicity of solutions for the bounce problem. J. Diff. Eq., 54(3):414–428, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Degiovanni, A. Marino, and M. Tosques. Evolution equations with lack of convexity. Nonlinear Anal. T.M.A, 9:1401–1443, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  9. G. Fournier, D. Lupo, M. Ramos, and M. Willem. Limit relative category and critical point theory. In U. K. C. K. R. T. Jones and H. O. Walther, editors, Dynamics Reported, pages 1–24. Springer, Berlin, 1994.

    Google Scholar 

  10. F. Giannoni. Bounce trajectories with one bounce point. Ann. Mat. Pura Appl., CLIX:101–115, 1991.

    Article  MathSciNet  Google Scholar 

  11. Marino and D. Mugnai. Asymptotical multiplicity and some reversed variational inequalities. Topol. Meth. Nonlinear Anal., 17:43–62, 2002.

    MathSciNet  Google Scholar 

  12. Marino and D. Mugnai. Asymptotically critical points and their multiplicity. Topol. Meth. Nonlinear Anal, 20:29–38, 2002.

    Google Scholar 

  13. Marino and C. Saccon. Some variational theorems of mixed type and elliptic problems with jumping nonlinearities. Ann. Scuola Norm. Sup. Pisa, XXV:631–665, 1997.

    MathSciNet  Google Scholar 

  14. Marino and C. Saccon. Nabla theorems and multiple solutions for some noncooperative elliptic systems. Topol. Meth Nonlinear Anal., 17:213–237, 2001.

    MATH  MathSciNet  Google Scholar 

  15. Marino and M. C. Saccon. Multiplicity results for the elastic bounce problem, to appear, N.S.

    Google Scholar 

  16. Marino and M. Tosques. Some variational problems with lack of convexity and some partial differential inequalities. In Method of Nonconvex Analysis, volume 1446 of Lecture Notes in Math., pages 58–83, Berlin, 1990. Springer. Varenna, 1989.

    Article  MathSciNet  Google Scholar 

  17. L. Penrose and R. Penrose. Puzzles for Christmas. New Scientist, 25 December 1958.

    Google Scholar 

  18. D. Percivale. Uniqueness IN elastic bounce problems. J. Diff. Eq., 54:1984, 1985.

    MathSciNet  Google Scholar 

  19. R J. Rauch. Illumination of bounded domains. Amer. Math. Monthly, pages 359–361, 1978.

    Google Scholar 

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Marino, A., Saccon, C. (2005). Asymptotically Critical Points and Multiple Solutions in the Elastic Bounce Problem. In: Giannessi, F., Maugeri, A. (eds) Variational Analysis and Applications. Nonconvex Optimization and Its Applications, vol 79. Springer, Boston, MA. https://doi.org/10.1007/0-387-24276-7_39

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