Asymmetric elliptic problems with indefinite weights
M. Arias; J. Campos; M. Cuesta; J.-P. Gossez
Annales de l'I.H.P. Analyse non linéaire (2002)
- Volume: 19, Issue: 5, page 581-616
- ISSN: 0294-1449
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topArias, M., et al. "Asymmetric elliptic problems with indefinite weights." Annales de l'I.H.P. Analyse non linéaire 19.5 (2002): 581-616. <http://eudml.org/doc/78555>.
@article{Arias2002,
author = {Arias, M., Campos, J., Cuesta, M., Gossez, J.-P.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {eigenvalue problem; Fučik spectrum; nonresonance problem},
language = {eng},
number = {5},
pages = {581-616},
publisher = {Elsevier},
title = {Asymmetric elliptic problems with indefinite weights},
url = {http://eudml.org/doc/78555},
volume = {19},
year = {2002},
}
TY - JOUR
AU - Arias, M.
AU - Campos, J.
AU - Cuesta, M.
AU - Gossez, J.-P.
TI - Asymmetric elliptic problems with indefinite weights
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2002
PB - Elsevier
VL - 19
IS - 5
SP - 581
EP - 616
LA - eng
KW - eigenvalue problem; Fučik spectrum; nonresonance problem
UR - http://eudml.org/doc/78555
ER -
References
top- [1] Aguilar A., Peral I., On a elliptic equation with exponential growth, Rend. Univ. Padova96 (1996) 143-175. Zbl0887.35055MR1438296
- [2] M. Alif, J.-P. Gossez, On the Fučik spectrum with indefinite weights, Diff. Int. Equations, to appear. Zbl1028.34074MR1859919
- [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. Zbl0633.35061
- [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. Toulouse9 (2000) 5-30. Zbl0971.35031MR1815938
- [5] Anane A., Gossez J.-P., Strongly nonlinear elliptic problems near resonance: A variational approach, Com. P. D. E.15 (1990) 1141-1159. Zbl0715.35029MR1070239
- [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. Zbl0854.35081MR1417265
- [7] Arias J., Campos M., Fučik spectrum of a singular Sturm–Liouville problem, Nonlinear Analysis T. M. A.27 (1996) 679-697. Zbl0857.34037MR1399068
- [8] Arias M., Campos J., Exact number of solutions of a one-dimensional Dirichlet problem with jumping nonlinearities, Differential Equations Dynam. Systems5 (1997) 139-161. Zbl0892.34017MR1657254
- [9] Arias M., Campos J., Cuesta M., Gossez J.-P., Sur certains problèmes elliptiques asymétriques avec poids indéfinis, C. R. Acad. Sci. Paris332 (2001) 215-218. Zbl0973.35147MR1817364
- [10] Arias M., Campos J., Gossez J.-P., On the antimaximum principle and the Fučik spectrum for the Neumann p-laplacian, Diff. Int. Equations13 (2000) 217-226. Zbl0979.35048MR1811956
- [11] Brezis H., Nirenberg L., Remarks on finding critical points, Com. Pure Appl. Math.44 (1991) 939-963. Zbl0751.58006MR1127041
- [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. Zbl0704.35048MR1018926
- [13] Cuesta M., Eigenvalue problems for the p-laplacian with indefinite weight, Elec. J. Diff. Equations2001 (2001) 1-9. Zbl0964.35110MR1836801
- [14] M. Cuesta, Minimax theorems on C1 manifolds via Ekeland variational principle, to appear. Zbl1072.58004MR1996922
- [15] Cuesta M., De Figueiredo D., Gossez J.-P., The beginning of the Fučik spectrum of the p-laplacian, J. Differential Equations159 (1999) 212-238. Zbl0947.35068MR1726923
- [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. Zbl0768.34025MR1181350
- [17] De Figueiredo D., Lectures on the Ekeland Variational Principle with Applications and Detours, TATA Institute, Springer-Verlag, 1989. Zbl0688.49011MR1019559
- [18] De Figueiredo D., Gossez J.-P., Strict monotonicity of eigenvalues and unique continuation, Com. P. D. E.17 (1992) 339-346. Zbl0777.35042MR1151266
- [19] De Figueiredo D., Gossez J.-P., On the first curve of the Fučik spectrum of an elliptic operator, Diff. Int. Equations7 (1994) 1285-1302. Zbl0797.35032MR1269657
- [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. Zbl0741.35013MR1103019
- [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. Zbl0809.35025MR1137903
- [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 Equations80 (1989) 1-13. Zbl0708.34019
- [23] Drabek P., Solvabiliy and Bifurcations of Nonlinear Equations, Pitman Research Notes in Mathematics, 264, 1992. Zbl0753.34002MR1175397
- [24] Drabek P., Robinson S., Resonance problems for the p-laplacian, J. Funct. Anal.169 (1999) 189-200. Zbl0940.35087MR1726752
- [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. Zbl0912.35064
- [26] Fonda A., Gossez J.-P., On a nonresonance condition for a semilinear elliptic problem, Diff. Int. Equations4 (1991) 945-951. Zbl0735.35054MR1123345
- [27] Friedlander L., Asymptotic behaviour of the eignevalues of the p-laplacian, Com. P. D. E.14 (1989) 1059-1069. Zbl0704.35108
- [28] Ghoussoub N., Duality and Perturbation Methods in Critical Point Theory, Cambridge Tracts in Mathematics, 107, Cambridge University Press, 1993. Zbl0790.58002MR1251958
- [29] Godoy T., Gossez J.-P., Paszka S., Antimaximum principle for elliptic problems with weight, Electr. J. Diff. Equations1999 (1999) 1-15. Zbl0920.35045
- [30] Gossez J.-P., Loulit A., A note on two notions of unique continuation, Bull. Soc. Math. Belgique45 (1993) 257-268. Zbl0828.35035MR1316725
- [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. Zbl0724.34048MR1059615
- [32] Hammerstein A., Nichtlineare Integralgleichungen nebst anwendungen, Acta Math.54 (1930) 117-176. Zbl56.0343.03MR1555304JFM56.0343.03
- [33] Jerison D., Kenig C., Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. Math.121 (1985) 463-494. Zbl0593.35119MR794370
- [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. Zbl0714.35029
- [35] Mahwin J., Ward J.R., Willem M., Variational methods and semilinear elliptic equations, Arch. Ration. Mech. Analysis95 (1986) 269-277. Zbl0656.35044MR853968
- [36] Reichel W., Walter W., Sturm–Liouville type problems for the p-laplacian under asymptotic nonresonance conditions, J. Differential Equations156 (1999) 50-70. Zbl0931.34059MR1701814
- [37] Rynne B., The Fučik spectrum of general Sturm–Liouville problems, J. Differential Equations161 (2000) 87-109. Zbl0976.34024MR1740358
- [38] Solimini S., Some remarks on the number of solutions of some nonlinear elliptic problems, Ann. I. H. P. Analyse Non linéaire2 (1985) 143-156. Zbl0583.35044MR794004
- [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. Zbl0583.47051MR768749
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