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Critical point theory and nonlinear differential equations

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References

  1. S. AHMAD, A.C. LAZER and J.L. PAUL, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976) 933–944.

    Article  MathSciNet  MATH  Google Scholar 

  2. A.CAPOZZI, D.FORTUNATO and A.SALVATORE, Periodic solutions of Lagrangian systems with bounded potential, to appear.

    Google Scholar 

  3. E.N. DANCER, On the use of asymptotic in nonlinear boundary value problems, Ann. Mat. Pura Appl. (4) 131 (1982) 167–185.

    Article  MathSciNet  MATH  Google Scholar 

  4. I. EKELAND, Nonconvex minimization problems, Bull. Amer. Math. Soc. (NS) 1 (1979) 443–474.

    Article  MathSciNet  MATH  Google Scholar 

  5. G. HAMEL, Über erzwungene Schwingungen bei endlichen Amplituden, Math. Ann. 86 (1922) 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. HAMMERSTEIN, Nichtlineare Integralgleichungen nebst Anwendungen, Acta Math., 54 (1930) 117–176.

    Article  MathSciNet  MATH  Google Scholar 

  7. D.LUPO and S.SOLIMINI, A note on a resonance problem, Proc. Royal Soc. Edinburgh, Ser. A, to appear.

    Google Scholar 

  8. J. MAWHIN and M. WILLEM, Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations, J. Diff. Equations 52 (1984) 264–287.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. MAWHIN and M. WILLEM, Variational methods and boundary value problems for vector second order differential equations and applications to the pendulum equation, in "Nonlinear Analysis and Optimization", Lect. Notes in Math. No 1107, Springer, Berlin, 1984, 181–192.

    Chapter  Google Scholar 

  10. J.MAWHIN and M.WILLEM, Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance, Ann. Inst. H. Poincaré, Analyse non-linéaire, to appear.

    Google Scholar 

  11. J.MAWHIN and M.WILLEM, "Critical Point Theory and Hamiltonian Systems", in preparation.

    Google Scholar 

  12. P.S. PALAIS, Critical point theory and the minimax principle, in Proc. Symp. Pure Math. vol. 15, Amer. Math. Soc., Providence, 1970, 185–212.

    MATH  Google Scholar 

  13. P. PUCCI and J. SERRIN, Extensions of the mountain pass theorem, J. Funct. Anal. 59 (1984) 185–210.

    Article  MathSciNet  MATH  Google Scholar 

  14. P.PUCCI and J.SERRIN, A mountain pass theorem, J. Differential Equations, 57 (1985).

    Google Scholar 

  15. P. RABINOWITZ, Some minimax theorems and applications to nonlinear partial differential equations, in "Nonlinear Analysis, a volume dedicated to E.H.Rothe", Academic Press, New York, 1978, 161–178.

    Google Scholar 

  16. S.SOLIMINI, On the solvability of some elliptic partial differential equations with the linear part at resonance, to appear.

    Google Scholar 

  17. J.R. WARD, A boundary value problem with a periodic nonlinearity, J. Nonlinear Analysis, to appear.

    Google Scholar 

  18. M. WILLEM, Oscillations forcées de systèmes hamiltoniens, Publ. Sémin. Analyse non linéaire Univ. Besançon, 1981.

    MATH  Google Scholar 

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Jaromír Vosmanský Miloš Zlámal

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© 1986 Equadiff 6 and Springer-Verlag

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Mawhin, J. (1986). Critical point theory and nonlinear differential equations. In: Vosmanský, J., Zlámal, M. (eds) Equadiff 6. Lecture Notes in Mathematics, vol 1192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076051

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  • DOI: https://doi.org/10.1007/BFb0076051

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  • Print ISBN: 978-3-540-16469-2

  • Online ISBN: 978-3-540-39807-3

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