A Sturm-Liouville theorem for nonlinear elliptic partial differential equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1966)
- Volume: 20, Issue: 3, page 543-582
- ISSN: 0391-173X
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topBerger, Melvyn S.. "A Sturm-Liouville theorem for nonlinear elliptic partial differential equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 20.3 (1966): 543-582. <http://eudml.org/doc/83392>.
@article{Berger1966,
author = {Berger, Melvyn S.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {partial differential equations},
language = {eng},
number = {3},
pages = {543-582},
publisher = {Scuola normale superiore},
title = {A Sturm-Liouville theorem for nonlinear elliptic partial differential equations},
url = {http://eudml.org/doc/83392},
volume = {20},
year = {1966},
}
TY - JOUR
AU - Berger, Melvyn S.
TI - A Sturm-Liouville theorem for nonlinear elliptic partial differential equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1966
PB - Scuola normale superiore
VL - 20
IS - 3
SP - 543
EP - 582
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/83392
ER -
References
top- 1 M. Berger, An eigenvatue problem for quasi-linear elliptic partial differential equations, Bull. Amer. Math. Soc.71, (1965) pp. 171-5. Zbl0125.33602MR179458
- 2 M. Berger, An eigenvalue problem for non-linear elliptic partial equations, Trans. Amer. Math. Soc.120 (1965) pp. 145-184. Zbl0142.08402MR181821
- 3 M. Berger, A Sturm-Liouville theorem for non-linear elliptic partial differential equations, Proc. Nat. Acad. Sci. USA53, (1965) pp. 1277-9. Zbl0173.43504MR188605
- 4 M. Berger, Ordicx spaces and non-linear, elliptic eigenvalue problems, Bull. Amer. Math. Soc.79 (1965) pp. 898-902. Zbl0133.05301MR185283
- 5 F. Browder, Variational methods for non-linear elliptic eigenvalue problems, Bull. Amer. Math. Soc.71 (1965) pp. 176-183. Zbl0135.15802MR179459
- 6 F. Browder, Ljusternik-Schnirelmann category and non-linear elliptic eigenvalue problems. Bull. Amer Math. Soc.71 (1965) pp. 644-8, Annals of Math.72 (1965) pp. 459-477 Zbl0136.12003MR178248
- 7 E.S. Citlanadze, The method of orthogonat trajectories and non linear operators of va riationat type in the space Lp. Amer. Math. Soe. Translation Series 2, Vol. 5 (1957) (pp. 305-333). MR83702
- 8 C. Dolph and G. Minty, On Non-linear Integral Equations of the Hammerstein type. Nonlinear Integral Equations edited by P. Anselone, University of Wisconsin Press1964, pp. 99-153. Zbl0123.29603MR161113
- 9 L. El'sgolc, Qualitative Mothods in Mathematical analysis, Vol. 12, Trans. of Math. Monographs A. M. S. 1964. Zbl0476.49001MR170048
- 10 I. Kolodner, Heavy Rotating String-A Non-dinear EigenvaLue Problem. Commun. Pure and Appl. Math. (1955) pp. 395-408. Zbl0065.17202MR71605
- 11 M. Krasnoselsky, Topological Methods in the theory of non-linear integral equations GITTL, Moscow1956, English trans. Macmillan, New York1964.
- 12 M. Krasnoselsky, Positive Solutions of Operator Equations, Noordhoff, Groningen1964.
- 13 O. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1963. Zbl0121.42701MR155093
- 14 N. Levinson, Positive eigenfunctions for Au + λ f (u) = 0, Arch. RAt. Mech. Anal. 11 (1962) pp. 258-72. Zbl0108.28902
- 15 J. Leray and J. Lions, Quelques resultats de Vishik. Bull. Soc. Math. France93,1965(97-107). Zbl0132.10502MR194733
- 16 J. Lions, Problemes aux limit dans les equations aux deriveee partielles, Lecture Notes1962. Universite de Montreal. MR251372
- 17 L. Ljusternik, Sur une class d'equations non-lineaires, Math. Sbornik N. S.2 (1937) pp. 1143-68.
- 18 L. Ljusternik, Quelques remarques supplementaires su les equations non-linaires de type de Sturm-Liouville, Math. Sb. N. S.4 (1938) pp. 227-232. JFM64.0439.01
- 19 A. Messiah, Quantum Mechanice Vol. II, North Holland. Amsterdam1962. Zbl0102.42602
- 20 Z. Nehari, Characteristic values associated with a class of non-linear differential equations, Acta Math.105 (1961) pp. 141-75. Zbl0099.29104MR123775
- 21 L. Rall, Variational Methods for Non-linear Integral Equations, Non-linear Integral Equations, ed. P. Anselone, University of Wisconsin Press, 1944 pp. 155-190. Zbl0123.31802MR166639
- 22 L. Schnirelmann, Uber eine neue Kombinatoriske InvarianteMonatsh. Math.371930 (131-4). Zbl56.1134.01JFM56.1134.01
- 23 J. Schwartz, Seneralizing the Ljusternik-Schnirelmann theory of critical points, Comm. Pure Appl. Math.17 (1964) pp. 807-15. Zbl0152.40801MR144212
- 24 M. Vainberg, Variational Methods for the investigation of non-linear operators GITTL, Moscow1959. Engl. trans. Holden DaySan Francisco1964.
- 25 M. Vishik, Quasilinear Strongly Elliptic Systems of Differential Equations in Divergence Form Trudy Mosk. Math. Obsc.121968 pp. 125-184. Zbl0144.36201
- 26 A. Wilansky, Functional Analysis, Blaisdell, New York1964. Zbl0136.10603MR170186
- 27 N. Meyers and J. Serrin, [to be published].
- 28 D. Cole, Transition in circular Couette flowJournal of Fluid Mechanics21, 1965, pp. 385-425. Zbl0134.21705
- 29 W. Velte, Stäbilitatsverhalten und Verzweigung stationer Lösungen der Navier-Stokasschera Gteichungen, Arch. Rat. Mech. Analy.17 pp. 97-125 (1964). Zbl0131.41808MR182240
- 30 Yamabe, On a Deformation af Riemannian Structures on Conipact Manifolds, Osaka Math. Jour.12 (1960), 21-37. Zbl0096.37201MR125546
- 31 H. Bethe, Intermediate Quantum Mechanincs, Benjamin1964New York. MR161579
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