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Nonlinear Hammerstein integral equations via local linking and mountain pass

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Abstract

In this paper we establish some results (single and multiple) for Hammerstein integral equations. The main results are based on the notion of local linking.

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References

  1. Benci, V.: A new approach to the Morse-Conley theory and some applications. Ann. Mat. Pura Appl. 158, 231–305 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chang, K.C.: Infinite-dimensional Morse theory and multiple solution problems. Progress in Nonlinear Differential Equations and their Applications, vol. 6. Birkhäuser, Boston (1993)

    MATH  Google Scholar 

  3. Krasnoselskii, M.A.: Topological Methods in the Theory of Nonlinear Integral Equations. Pergamon, Oxford (1964)

    Google Scholar 

  4. Li, S., Willem, M.: Applications of local linking to critical point theory. J. Math. Anal. Appl. 189, 6–32 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, F., Li, Y., Liang, Z.: Existence of solutions to nonlinear Hammerstein integral equations and applications. J. Math. Anal. Appl. 323, 209–227 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu, J.Q., Li, S.H.: An existence theorem for multiple critical points and its application. Kexue Tongbao (Chinese) 29, 1025–1027 (1984)

    MathSciNet  Google Scholar 

  7. O’Regan, D.: Multiplicity results for sublinear and superlinear Hammerstein integral equations via Morse theory. Commun. Appl. Anal. 13, 385–394 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Perera, K., Agarwal, R.P., O’Regan, D.: Morse-theoretic aspects of p-Laplacian type operators. Mathematical Surveys and Monographs, vol. 161. Am. Math. Soc., Providence (2010)

    Google Scholar 

  9. Precup, R.: Methods in Nonlinear Integral Equations. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  10. Rabinowitz, P.: Minimax Methods in Critical Point Theory Will Applications to Differential Equations. CBMS Reg. Conf. Ser. Math., vol. 65. Am. Math. Soc., Providence (1986)

    Google Scholar 

  11. Young, N.: An Introduction to Hilbert Spaces. Cambridge University Press, Cambridge (1989)

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

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  1. Donal O’Regan
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Correspondence to Donal O’Regan.

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O’Regan, D. Nonlinear Hammerstein integral equations via local linking and mountain pass. Rend. Circ. Mat. Palermo 60, 357–364 (2011). https://doi.org/10.1007/s12215-011-0056-0

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  • DOI: https://doi.org/10.1007/s12215-011-0056-0

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