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Multiple solutions for semilinear resonant elliptic problems with discontinuous nonlinearities via nonsmooth double linking theorem

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Abstract

In the present paper, some multiplicity results for semilinear resonant elliptic problems with discontinuous nonlinearities are obtained by using our extended double linking theorem.

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References

  1. Chang K.: Variational methods for non-differential functions and their applications to partial differential equations. J. Math. Anal. Appl. 80, 102–129 (1981)

    Article  Google Scholar 

  2. Chang K.: Critical Point Theory and its Applications. Shanghai Scientific and Technological Literature Publishing House, Shanghai (1986)

    Google Scholar 

  3. Clarke F.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)

    Google Scholar 

  4. Denkowski Z., Gasinski L., Papageorgiou N.: Nontrivial solutions for resonant hemivariational inequalities. J. Glob. Optim. 34, 317–337 (2006)

    Article  Google Scholar 

  5. Filippakis M., Gasinski L., Papageorgiou N.S.: Multiple positive solutions for eigenvalue problems of Hemivariational inequalities. Positivity 10, 491–515 (2006)

    Article  Google Scholar 

  6. Gasinki L., Papageorgiou N.: Nonsmooth critical point theory and nonlinear boundary value problems. Chapman Hall/CRC, Boca Raton (2005)

    Google Scholar 

  7. Gasinki L., Motreanu D., Papageorgiou N.: Multiplicity of nontrivial solutions for elliptic equations with nonsmooth potential and resonance at higher eigenvalues. Proc. Indian Acad. Sci. 116, 233–255 (2006)

    Article  Google Scholar 

  8. Kourogenis N.C., Papageorgiou N.S.: Nonsmooth critical point theory and nonlinear elliptic equations at resonance. J. Aust. Math. Soc. 69, 245–271 (2000)

    Article  Google Scholar 

  9. Kyritsi S.Th., Papageorgiou N.S.: Solvability of semilinear hemivariational inequalities at resonance using generalized Landesman-CLazer conditions. Monatsh. Math. 142, 227–241 (2004)

    Article  Google Scholar 

  10. Marano S.A., Motreanu D.: On a three critical points theorem for non-differential functions and applications to nonlinear boundary value problems. Nonlinear Analy. TMA 48, 37–52 (2002)

    Article  Google Scholar 

  11. Naniewicz Z., Panagiotopoulos P.: Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, NewYork (1995)

    Google Scholar 

  12. Papageorgiou E.H., Papageorgiou N.S.: Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems. Czechoslov. Math. J. 54(129), 347–371 (2004)

    Article  Google Scholar 

  13. Schechter M., Tintarev K.: Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems. Bull. Soc. Math. Belg. 44, 249–261 (1994)

    Google Scholar 

  14. Schechter M., Zou W.: Double linking theorem and multiple solutions. J. Funct. Anal. 205, 37–61 (2003)

    Article  Google Scholar 

  15. Teng K., Wu X.: Multiplicity results for semilinear resonance elliptic problems with discontinuous nonlinearities. Nonlinear Anal. TMA 68, 1652–1667 (2008)

    Google Scholar 

  16. Zeidler E.: Nonlinear Functional Analysis and Its Applications, vol. II/B. Springer-Verlag, Berlin (1985)

    Google Scholar 

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Correspondence to Kaimin Teng.

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Teng, K. Multiple solutions for semilinear resonant elliptic problems with discontinuous nonlinearities via nonsmooth double linking theorem. J Glob Optim 46, 89–110 (2010). https://doi.org/10.1007/s10898-009-9411-5

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  • DOI: https://doi.org/10.1007/s10898-009-9411-5

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