Skip to main content

Mountain Pass and Linking Type Solutions for Semilinear Dirichlet Forms

  • Chapter
Recent Trends in Nonlinear Analysis

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 40))

  • 215 Accesses

Summary

Using mountain pass and linking type techniques, we obtain some existence results of (possibly positive) solutions for certain semilinear problems associated with general Dirichlet forms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.AmbrosettiP. H.Rabinowitz:Dual variational methods in critical point theory and applicationsJ. Funct. Anal.14 (1973), 349–381

    Article  MathSciNet  MATH  Google Scholar 

  2. I.BirindelliI.Capuzzo DolcettaA. Cutri:Liouville theorems for semilinear equations on the Heisenberg groupAnn. Inst. H. Poincare, Analyse Nonlineaire14, 3 (1997), 295–308

    Article  MATH  Google Scholar 

  3. M.BiroliU.Mosco:Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spacesRend. Accad. Naz. Lincei9 (1995), 37–44

    MathSciNet  Google Scholar 

  4. M.BiroliU.Mosco:Sobolev inequalities on homogenous spacesPotential Anal. 4 (1995), 311–324

    Article  MathSciNet  MATH  Google Scholar 

  5. M.BiroliN.Tchou:Asymptotic behaviour of relaxed Dirichlet problems involving a Dirichlet-Poincaré formJ. Anal. Appl.16 2 (1997), 281–309

    MathSciNet  MATH  Google Scholar 

  6. M.BiroliS.Tersian: On the existence of nontrivial solutions to a semilinear equation relative to a Dirichlet form, to appear

    Google Scholar 

  7. P.CaldiroliR.Musina:On a variational degenerate elliptic problemto appear

    Google Scholar 

  8. P.CaldiroliR.Musina:On the existence of extremal functions for a weighted Sobolev embedding with critical exponentto appear

    Google Scholar 

  9. G.Citti:Semilinear Dirichlet problem involving critical exponent for the Kohn LaplacianAnnali Mat. Pura Appl.169 (1995), 375–392

    Article  MathSciNet  MATH  Google Scholar 

  10. G.DalmasoV.DiciccoL.NotarantonioN.Tchou:Limits of variational problems of Dirichlet forms in varying domainsJ. Math. Pure Appl. 77 (1998), 89–116

    Google Scholar 

  11. J. E.FabesC.KenigR.Serapioni:The local regularity of solutions of degenerate elliptic equationsComm. Part. Duff. Equ. 7 (1982), 77–116

    Article  MathSciNet  MATH  Google Scholar 

  12. K. J.Falconer:Semilinear partial differential equations on self-similar fractalsto appear

    Google Scholar 

  13. K. J.FalconerJ.Hu:Multiple solutions for a class of nonlinear elliptic equations on the Sierpiriski Gasketto appear

    Google Scholar 

  14. M.FukushimaT.Shima:On a spectral analysis for the Sierpiriski Gasket,Potential Anal.1 (1992), 1–35

    Article  MathSciNet  MATH  Google Scholar 

  15. N.GarofaloE.Lanconelli:Existence and non existence results for semilinear equations on the Heisenberg groupIndiana Univ. Math. J.41 (1992), 71–98

    Article  MathSciNet  MATH  Google Scholar 

  16. D.Jerison:The Poincare inequality for vector fields satisfying the Hermander conditionDuke Math. J.53 (1986), 503–523

    Article  MathSciNet  MATH  Google Scholar 

  17. E.LanconelliE.Uguzzoni:Asymptotic behaviour and non existence theorem for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg groupBoll. Unione Mat. Ital.B-8 (1998), 139–168

    MathSciNet  Google Scholar 

  18. U.Mosco:Variational metrics on selfsimilar fractalsC. R. Acad. Sci. Paris321 (1995), 715–720

    MathSciNet  MATH  Google Scholar 

  19. U.Mosco:Dirichlet forms and self-similarityAMS/IP Studies Adv. Math.8 (1998), 117–155

    MathSciNet  Google Scholar 

  20. U.Mosco:Spectral properties of fractal structuresRend. Accad. Naz. Lincei, to appear

    Google Scholar 

  21. D.Passaseo:Some concentration phenomena in degenerate semilinear elliptic problemsNonlin. Anal. TMA24 7 (1995), 1011–1025

    Article  MathSciNet  MATH  Google Scholar 

  22. P. H.Rabinowitz:Minimax Methods in Critical Point Theory with Applications to Differential EquationsCBMS Regional Conf. Series Math.65Amer. Math. Soc., Providence RI 1986

    Google Scholar 

  23. F.Uguzzoni:A non existence theorem for a semilinear Dirichlet problem involving critical exponential on half-spaces of the Heisenberg groupNonlin. Diff. Equ. Appl., to appear

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Alfonso Vignoli on the occasion of his 60th birthday

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Basel AG

About this chapter

Cite this chapter

Matzeu, M. (2000). Mountain Pass and Linking Type Solutions for Semilinear Dirichlet Forms. In: Appell, J. (eds) Recent Trends in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 40. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8411-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8411-2_20

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9556-9

  • Online ISBN: 978-3-0348-8411-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics