Summary
We use a new form of the mountain pass lemma to extend results on superlinear boundary value problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[AR] A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Func. Anal.14 349–381 (1973)
[AT] S. Alama and G. Tarantello, On semilinear elliptic equations with indefinite nonlinearities, Calculus of Variations, to appear
[ALP] S. Ahmad, A.C. Lazer, J. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J.25, 933–944 (1976)
[CM1] D.G. Costa and C.A. Magalhaes, Variational elliptic problems which are nonquadratic at infinity, Trabelhos de Mat.250, 1–14 (1991)
[CM2] D.G. Costa and C.A. Magalhaes, Un probleme elliptique nonquadratique a l'infini, C.R. Acad. Sci. Paris,315, 1059–1062 (1992)
[dFM] D.G. de Figueiredo and I. Massabo, Semilinear elliptic equations with primitive of the nonlinearity interacting with the first eigenvalue, J. Math. Anal & Appl.,156, 381–394 (1991)
[FG] A. Fonda and J.-P. Gossez, semicoercive variational problems at resonance: an abstract approach, Louvain-la-Neuve, Report No.143, 1988
[LL] E.A. Landesman and A.C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech.19, 609–623 (1970)
[LM] A.C. Lazer and P.J. McKenna, Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues, Comm. P.D.E., I,10, 107–150 (1985), II,11, 1653–1676 (1986)
[MWW] J. Mawhin, J.R. Ward and M. Willem, Variational methods and semilinear elliptic equations, Arch. Rat. Mech. Anal.95, 269–277 (1986)
[R] P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, Conf. Board of Math. Sci. Reg. Conf. Ser. in Math., No.65, Amer. Math. Soc., 1986
[Sc1] M. Schechter, New saddle point theorems. Proceedings of an International Symposium on Generalized Functions and their Applications, Varanasi, India, December 23–26, 1991. Plenum, N.Y., 1993, pp. 213–219
[Sc2] M. Schechter, A generalization of the saddle point method with applications, Annales Polonici Mathematici,57, 269–281 (1992)
[Sc3] M. Schechter, Critical points over splitting subspaces, Nonlinearity,6, 417–427 (1993)
[Sc4] M. Schechter, Splitting subspaces and critical points, Applicable Analysis,49, 33–48 (1993)
[Sc5] M. Schechter, The intrinsic mountain pass, to appear
[Sc6] M. Schechter, Critical points when there is no saddle point geometry, preprint.
[Sc7] M. Schechter, A bounded mountain pass lemma without the (PS) condition and applications, Trans. Amer. Math. Soc.,331, 681–703 (1992)
[Si] E.A. de B.e. Silva, Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Analysis TMA,16, 455–477 (1991)
[ST] M. Schechter and K. Tintarev, Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems, Bull. Soc. Math. Belg.44, 249–261 (1992)
Author information
Authors and Affiliations
Additional information
Research supported in part by an NSF grant
This article was processed by the author using the LATEX style filecljour1m from Springer-Verlag.
Rights and permissions
About this article
Cite this article
Schechter, M. Superlinear elliptic boundary value problems. Manuscripta Math 86, 253–265 (1995). https://doi.org/10.1007/BF02567993
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02567993