Results in Mathematics

, Volume 14, Issue 1–2, pp 138–146 | Cite as

Landesman-Lazer Type Problems At An Eigenvalue Of Odd Multiplicity

  • Jean Mawhin
  • Klaus Schmitt


This paper is concerned with sublinear perturbations of resonant linear problems (Landesman-Lazer problems). We establish some a priori bounds and use these together with Leray-Schauder continuation and bifurcation arguments to obtain extensions of some known results where the nonlinear perturbation terms are bounded.

Key Words

problems at resonance bifurcation from infinity sublinear perturbation 

1980 Mathematics subject classifications

35B15 47H15 58E07 


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  1. [ALP]
    S. Ahmad, A. Lazer, and J. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933–944.MathSciNetMATHCrossRefGoogle Scholar
  2. [BH]
    H. Brezis and A. Haraux, Image d’une somme d’operateurs monotones et applications, Israel J. Math. 23 (1976), 165–186.MathSciNetMATHCrossRefGoogle Scholar
  3. [CJSS]
    D. Costa, H. Jeggle, R. Schaaf, and K. Schmitt, Periodic perturbations of linear problems at resonance.Google Scholar
  4. [F]
    S. Fucik, “Solvability of Nonlinear Equations and Boundary Value Problems,” D. Reidel Publishing Co., Boston, 1980.MATHGoogle Scholar
  5. [GM]
    R. Gaines and J. Mawhin, “Coincidence Degree and Nonlinear Differential Equations,” Springer Lecture Notes in Math 568, Berlin, New York, 1977.Google Scholar
  6. [LL]
    E. Landesman and A. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609–623.MathSciNetMATHGoogle Scholar
  7. [PS]
    H. Peitgen and K. Schmitt, Global analysis of two-parameter elliptic eigenvalue problems, Trans. Amer. Math. Soc. 283 (1984), 57–95.MathSciNetMATHCrossRefGoogle Scholar
  8. [R]
    P. Rabinowitz, On bifurcation from infinity, J. Diff. Eqs. 14 (1973), 462–475.MathSciNetMATHCrossRefGoogle Scholar
  9. [SS]
    R. Schaaf and K. Schmitt, A class of nonlinear Sturm-Liouville problems with infinitely many solutions, Trans. Amer. Math. Soc. (to appear).Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 1988

Authors and Affiliations

  • Jean Mawhin
    • 1
  • Klaus Schmitt
    • 2
  1. 1.Institute de Mathématique Pure et AppliquéeUniversité Catholique de LouvainLouvain-La-NeuveBelgium
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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