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Deformation in locally convex topological linear spaces

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Abstract

We are concerned with a deformation theory in locally convex topological linear spaces. Aspecial “nice” partition of unity is given. This enables us to construct certain vector fields which are locally Lipschitz continuous with respect to the locally convex topology. The existence, uniqueness and continuous dependence of flows associated to the vector fields are established. Deformations related to strongly indefinite functionals are then obtained. Finally, as applications, we prove some abstract critical point theorems.

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References

  1. Benci, V., Rabinowitz, P. H., Critical point theorems for indefinite functionals, Inv. Math., 1979, 52: 241–273.

    Article  MATH  MathSciNet  Google Scholar 

  2. Rabinowitz, P. H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. in Math. 65 AMS, 1986.

  3. Larsen, R., Functional Analysis, New York: Marcel Dekker, Inc., 1973.

    MATH  Google Scholar 

  4. Kryszewski, W., Szulkin, A., Generalized linking theorem with an application to semilinear Schödinger equation, Adv. Diff. Eqs., 1998, 3: 441–472.

    MATH  MathSciNet  Google Scholar 

  5. Ding, Y. H., Girardi, M., Infinitely many homoclinic orbits of a Hamitonian system with symmetry, Nonlinear Analysis, TMA, 1999, 38: 391–415.

    Article  MathSciNet  Google Scholar 

  6. Ding, Y. H., Willem, M., Homoclinic orbits of a Hamiltonian system, Z. Angew. Math. Phys., 1999, 50: 759–778.

    Article  MATH  MathSciNet  Google Scholar 

  7. Graff, R. A., Elements of Non-Linear Functional Analysis, Memoirs AMS, 1978, Vol. 16, No. 206.

  8. Zhang, J. Y., Geometric Theory of Ordinary Equations and Bifurcations (in Chinese), Beijing: Beijing Univ. Press, 1981.

    Google Scholar 

  9. Cerami, G., Un criterio di esistenza per i punti critici su varietá illimitate, Istit. Lombardo Accad. Sci. Lett. Rend. A, 1978, 112: 332–336.

    MathSciNet  Google Scholar 

  10. Bartsch, T., Ding, Y. H., On a nonlinear Schrödinger equations, Math. Ann., 1999, 313: 15–37.

    Article  MATH  MathSciNet  Google Scholar 

  11. Bartsch, T., Ding, Y. H., Homoclinic solutions of an infinite-dimensional Hamiltonian system, Math. Z., 2002, 240: 289–310.

    Article  MATH  MathSciNet  Google Scholar 

  12. Dowker, C. H., An embedding theorem for paracompact metric spaces, Duke Math. J., 1947, 14: 639–645.

    Article  MATH  MathSciNet  Google Scholar 

  13. Michael, E., A note on paracompact spaces, Proc. Amer. Math. Soc., 1953, 4: 831–838.

    Article  MATH  MathSciNet  Google Scholar 

  14. Ambrosetti, A., Rabinowitz, P. H., Dual variational methods in critical point theory and applications, J. Funct. Anal., 1973, 14: 349–381.

    Article  MATH  MathSciNet  Google Scholar 

  15. Chang, K. C., Critical Point Theory and Its Applications (in Chinese), Shanghai: Shanghai Sci. Techn. Press, 1986.

    Google Scholar 

  16. Chang, K. C., Infinitely Dimensional Morse Theory and Multiple Solution Problems, Birkäuser, 1993.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Yanheng Ding

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  1. Yanheng Ding
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Correspondence to Yanheng Ding.

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Ding, Y. Deformation in locally convex topological linear spaces. Sci. China Ser. A-Math. 47, 687 (2004). https://doi.org/10.1007/BF03036994

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  • DOI: https://doi.org/10.1007/BF03036994

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