Kodai Mathematical Journal

Nonsmooth critical point theory and nonlinear elliptic equations at resonance

Nikolaos C. Kourogenis and Nikolaos S. Papageorgiou

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Kodai Math. J., Volume 23, Number 1 (2000), 108-135.

First available in Project Euclid: 23 January 2006

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Zentralblatt MATH identifier

Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 35B38: Critical points 35J60: Nonlinear elliptic equations 47J30: Variational methods [See also 58Exx]


Kourogenis, Nikolaos C.; Papageorgiou, Nikolaos S. Nonsmooth critical point theory and nonlinear elliptic equations at resonance. Kodai Math. J. 23 (2000), no. 1, 108--135. doi:10.2996/kmj/1138044160. https://projecteuclid.org/euclid.kmj/1138044160

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  • [1] ADAMS, R., Sobolev Spaces, Academic Press, New York, 1975.
  • [2] AHMAD, S., Multiple nontvial solutions of resonant and nonresonant asymptotically linea problems, Proc. Amer. Math. Soc, 96 (1986), pp. 405-409.
  • [3] AHMAD, S., LAZER, A. AND PAUL, J., Elementary critical point theory and perturbations o elliptic boundary value problems at resonance, Indiana Univ. Math. J., 25 (1976), pp. 933-944.
  • [4] BARTOLO, P., BENCI, V AND FORTUNATO, D., Abstract critical point theorems and application to some nonlinear problems with "strong resonance" at infinity, Nonlinear Appl., 9 (1983), pp. 981-1012.
  • [5] BREZIS, H. and NIRENBERG, L., Remarks on finding critical points, Comm. Pure Appl. Math., 64 (1991), pp. 939-963
  • [6] CERAMI, G., Un cteo di esistenza per I punti ctici su vaeta illimitate, Rend. Institut Lombardo Sci. Lett., 112 (1978) pp. 332-336.
  • [7] CHANG, K. -C, Variational methods for non-differentiable functionals and their applications t partial differential equations, J. Math. Anal. Appl., 80 (1981), pp. 102-129.
  • [8] CLARKE, F H., Optimization and Nonsmooth Analysis, Wiley, New York, 1983
  • [9] GHOUSSOUB, N., Duality and Perurbation Methods in Critical Point Theory, Cambridg University Press, Cambridge, 1993.
  • [10] GONCALVES, J. AND MIYAGAKI, O., Multiple nontvial solutions of semilinear strongly resonan elliptic equations, Nonlinear Anal., 19 (1992), pp. 43-52.
  • [11] GONCALVES, J. AND MIYAGAKI, O., Three solutions for a strongly resonant elliptic problems, Nonlinear Anal., 24 (1995), pp. 265-272
  • [12] Hu, S. AND PAPAGEORGIOU, N. S., Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, 199
  • [13] KESAVAN, S., Topics in Functional Analysis and Applications, Wiley, New York, 1989
  • [14] KOUROGENIS, N. C. AND PAPAGEORGIOU, N. S., Discontinuous quasilinear elliptic problems a resonance, Colloq. Math., 78 (1998), pp. 213-223.
  • [15] KOUROGENIS, N. C. AND PAPAGEORGIOU, N. S., Multiple solutions for nonlinear discontinuou elliptic equations near resonance, Colloq. Math., 81 (1999), pp. 80-99.
  • [16] KOUROGENIS, N. C. AND PAPAGEORGIOU, N. S., Three nontvial solutions for a quasilinea elliptic differential equation at resonance with discontinuous right hand side, J. Math. Anal. Appl., 238 (1999), pp. 477-490.
  • [17] KOUROGENIS, N. C. AND PAPAGEORGIOU, N. S., Multiple solutions for nonlinear discontinuou strongly resonant problems, to appear in J. Math. Soc. Japan.
  • [18] LANDESMAN, E., ROBINSON, S. AND RUMBOS, A., Multiple solutions of semilinear ellipti problems at resonance, Nonlinear Anal., 24 (1995), pp. 1049-1059.
  • [19] LIEBERMAN, G., Boundary regularity for solutions of degenerate elliptic equations, Nonlinea Anal., 12 (1988), pp. 1203-1219.
  • [20] LINDQVIST, P., On the equation div(\\Dx\\p~2Dx) + \x\p~2x = 0, Proc. Amer. Math. Soc, 109 (1990), pp. 157-164
  • [21] RABINOWITZ, P., Minimax Methods in Critical Point Theory with Applications to Differentia Equations, CBMS Regional Conf. Ser. in Math., 65, Amer. Math. Soc, Providence, R. I., 1986.
  • [22] SOLIMINI, S., On the solvability of some elliptic partial differential equations with linear part a resonance, J. Math. Anal. Appl., 117 (1986), pp. 138-152.
  • [23] THEWS, K., Nontvial solutions of elliptic equations at resonance, Proc. Royal Soc. Edin burgh Sect. A, 85 (1990), pp. 119-129.
  • [24] TOLKSDORF, P., Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), pp. 126-150
  • [25] WARD, J., Applications of critical point theory to weakly nonlinear boundary value problem at resonance, Houston J. Math., 10 (1984), pp. 291-305.
  • [26] ZHONG, C. -K., On Ekeland's vaational principle and a minimax theorem, J. Math. Anal Appl., 205 (1997), pp. 239-250.