Asymmetric elliptic problems with indefinite weights
Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 5, p. 581-616
@article{AIHPC_2002__19_5_581_0,
     author = {Arias, M. and Campos, J. and Cuesta, M. and Gossez, J.-P.},
     title = {Asymmetric elliptic problems with indefinite weights},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {19},
     number = {5},
     year = {2002},
     pages = {581-616},
     zbl = {1016.35054},
     mrnumber = {1922470},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_5_581_0}
}
Arias, M.; Campos, J.; Cuesta, M.; Gossez, J.-P. Asymmetric elliptic problems with indefinite weights. Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 5, pp. 581-616. http://www.numdam.org/item/AIHPC_2002__19_5_581_0/

[1] Aguilar A., Peral I., On a elliptic equation with exponential growth, Rend. Univ. Padova 96 (1996) 143-175. | Numdam | MR 1438296 | Zbl 0887.35055

[2] M. Alif, J.-P. Gossez, On the Fučik spectrum with indefinite weights, Diff. Int. Equations, to appear. | MR 1859919 | Zbl 1028.34074

[3] Anane A., Etude des valeurs propres et de la résonance pour l'opérateur p-laplacien, Thèse de Doctorat, Université Libre de Bruxelles, 1987, See also C. R. Acad. Sci. Paris 305 (1987) 725-728. | Zbl 0633.35061

[4] Anane A., Chakrone O., Sur un théorème de point critique et application à un problème de non-résonance entre deux valeurs propres du p-laplacien, Ann. Fac. Sc. Toulouse 9 (2000) 5-30. | Numdam | MR 1815938 | Zbl 0971.35031

[5] Anane A., Gossez J.-P., Strongly nonlinear elliptic problems near resonance: A variational approach, Com. P. D. E. 15 (1990) 1141-1159. | MR 1070239 | Zbl 0715.35029

[6] Anane A., Tsouli N., On the second eigenvalue of the p-laplacian, in: Benkirane A., Gossez J.-P. (Eds.), Nonlinear Partial Differential Equation, Pitman Res. Notes in Math., 343, 1996, pp. 1-9. | MR 1417265 | Zbl 0854.35081

[7] Arias J., Campos M., Fučik spectrum of a singular Sturm-Liouville problem, Nonlinear Analysis T. M. A. 27 (1996) 679-697. | MR 1399068 | Zbl 0857.34037

[8] Arias M., Campos J., Exact number of solutions of a one-dimensional Dirichlet problem with jumping nonlinearities, Differential Equations Dynam. Systems 5 (1997) 139-161. | MR 1657254 | Zbl 0892.34017

[9] Arias M., Campos J., Cuesta M., Gossez J.-P., Sur certains problèmes elliptiques asymétriques avec poids indéfinis, C. R. Acad. Sci. Paris 332 (2001) 215-218. | MR 1817364 | Zbl 0973.35147

[10] Arias M., Campos J., Gossez J.-P., On the antimaximum principle and the Fučik spectrum for the Neumann p-laplacian, Diff. Int. Equations 13 (2000) 217-226. | MR 1811956 | Zbl 0979.35048

[11] Brezis H., Nirenberg L., Remarks on finding critical points, Com. Pure Appl. Math. 44 (1991) 939-963. | MR 1127041 | Zbl 0751.58006

[12] Costa D., Oliveira A., Existence of solutions for a class of semilinear problems at double resonance, Boll. Soc. Brasil. Mat. 19 (1988) 21-37. | MR 1018926 | Zbl 0704.35048

[13] Cuesta M., Eigenvalue problems for the p-laplacian with indefinite weight, Elec. J. Diff. Equations 2001 (2001) 1-9. | MR 1836801 | Zbl 0964.35110

[14] M. Cuesta, Minimax theorems on C1 manifolds via Ekeland variational principle, to appear. | MR 1996922 | Zbl 1072.58004

[15] Cuesta M., De Figueiredo D., Gossez J.-P., The beginning of the Fučik spectrum of the p-laplacian, J. Differential Equations 159 (1999) 212-238. | MR 1726923 | Zbl 0947.35068

[16] Cuesta M., Gossez J.-P., A variational approach to nonresonance with respect to the Fučik spectrum, Nonlinear Analysis T. M. A. 19 (1992) 487-500. | MR 1181350 | Zbl 0768.34025

[17] De Figueiredo D., Lectures on the Ekeland Variational Principle with Applications and Detours, TATA Institute, Springer-Verlag, 1989. | MR 1019559 | Zbl 0688.49011

[18] De Figueiredo D., Gossez J.-P., Strict monotonicity of eigenvalues and unique continuation, Com. P. D. E. 17 (1992) 339-346. | MR 1151266 | Zbl 0777.35042

[19] De Figueiredo D., Gossez J.-P., On the first curve of the Fučik spectrum of an elliptic operator, Diff. Int. Equations 7 (1994) 1285-1302. | MR 1269657 | Zbl 0797.35032

[20] De Figueiredo D., Massabo I., Semilinear elliptic equations with the primitive of the nonlinearity interacting with the first eigenvalue, J. Math. Anal. Appl. 156 (1991) 381-394. | MR 1103019 | Zbl 0741.35013

[21] De Figueiredo D., Miyagaki O., Semilinear elliptic equations with the primitive of the nonlinearity away from the spectrum, Nonlinear Analysis T. M. A. 17 (1991) 1201-1219. | MR 1137903 | Zbl 0809.35025

[22] Del Pino M., Elgueta M., Manasevich R., A homotopy deformation along p of a Leray-Schauder degree result and existence for (|u′|p−2u′)′+f(t,u)=0, u(0)=u(T)=0, p>1, J. Differential Equations 80 (1989) 1-13. | Zbl 0708.34019

[23] Drabek P., Solvabiliy and Bifurcations of Nonlinear Equations, Pitman Research Notes in Mathematics, 264, 1992. | MR 1175397 | Zbl 0753.34002

[24] Drabek P., Robinson S., Resonance problems for the p-laplacian, J. Funct. Anal. 169 (1999) 189-200. | MR 1726752 | Zbl 0940.35087

[25] Fleckinger J., Hernandez J., Takaǩ P., De Thelin F., Uniqueness and positivity of solutions of equations with the p-laplacian, in: Caristi G., Mitidieri E. (Eds.), Reaction Diffusion Systems, Lect. Notes P. Appl. Math., 194, M. Dekker, 1998, pp. 141-155. | Zbl 0912.35064

[26] Fonda A., Gossez J.-P., On a nonresonance condition for a semilinear elliptic problem, Diff. Int. Equations 4 (1991) 945-951. | MR 1123345 | Zbl 0735.35054

[27] Friedlander L., Asymptotic behaviour of the eignevalues of the p-laplacian, Com. P. D. E. 14 (1989) 1059-1069. | Zbl 0704.35108

[28] Ghoussoub N., Duality and Perturbation Methods in Critical Point Theory, Cambridge Tracts in Mathematics, 107, Cambridge University Press, 1993. | MR 1251958 | Zbl 0790.58002

[29] Godoy T., Gossez J.-P., Paszka S., Antimaximum principle for elliptic problems with weight, Electr. J. Diff. Equations 1999 (1999) 1-15. | Zbl 0920.35045

[30] Gossez J.-P., Loulit A., A note on two notions of unique continuation, Bull. Soc. Math. Belgique 45 (1993) 257-268. | MR 1316725 | Zbl 0828.35035

[31] Gossez J.-P., Omari P., Nonresonnance with respect tot the Fučik spectrum for periodic solutions of second order ordinary differential equations, Nonlinear Analysis T. M. A. 14 (1990) 1079-1104. | MR 1059615 | Zbl 0709.34037 | Zbl 0724.34048

[32] Hammerstein A., Nichtlineare Integralgleichungen nebst anwendungen, Acta Math. 54 (1930) 117-176. | JFM 56.0343.03 | MR 1555304

[33] Jerison D., Kenig C., Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. Math. 121 (1985) 463-494. | MR 794370 | Zbl 0593.35119

[34] Lindqvist P., On the equation div (|∇u|p−2∇u)+λ|u|p−2u=0, Proc. Amer. Math. Soc. 109 (1990) 157-166, Addendum, Proc. Amer. Math. Soc. 116 (1992) 583-584. | Zbl 0787.35027 | Zbl 0714.35029

[35] Mahwin J., Ward J.R., Willem M., Variational methods and semilinear elliptic equations, Arch. Ration. Mech. Analysis 95 (1986) 269-277. | MR 853968 | Zbl 0656.35044

[36] Reichel W., Walter W., Sturm-Liouville type problems for the p-laplacian under asymptotic nonresonance conditions, J. Differential Equations 156 (1999) 50-70. | MR 1701814 | Zbl 0931.34059

[37] Rynne B., The Fučik spectrum of general Sturm-Liouville problems, J. Differential Equations 161 (2000) 87-109. | MR 1740358 | Zbl 0976.34024

[38] Solimini S., Some remarks on the number of solutions of some nonlinear elliptic problems, Ann. I. H. P. Analyse Non linéaire 2 (1985) 143-156. | Numdam | MR 794004 | Zbl 0583.35044

[39] Touzani A., Quelques résultats sur le Ap-laplacien avec poids indéfini, Thèse de Doctorat, Université Libre de Bruxelles, 1992.

[40] Zeidler E., Nonlinear Functional Analysis and its Applications, Vol. III (Variational Methods and Optimization), Springer-Verlag, 1984. | MR 768749 | Zbl 0583.47051