A Sturm-Liouville theorem for nonlinear elliptic partial differential equations

Berger, Melvyn S.

Berger, Melvyn S.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 20 (1966) no. 3, pp. 543-582.

MR 211299 | Zbl 0147.09503

⇒ corrigé par Corrections to my paper “A Sturm-Liouville theorem for nonlinear elliptic partial differential equations”

@article{ASNSP_1966_3_20_3_543_0,
     author = {Berger, Melvyn},
     title = {A Sturm-Liouville theorem for nonlinear elliptic partial differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {543--582},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 20},
     number = {3},
     year = {1966},
     zbl = {0147.09503},
     mrnumber = {211299},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1966_3_20_3_543_0/}
}

Berger, Melvyn S. A Sturm-Liouville theorem for nonlinear elliptic partial differential equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 20 (1966) no. 3, pp. 543-582. http://www.numdam.org/item/ASNSP_1966_3_20_3_543_0/

Bibliographie

1 M. Berger, An eigenvatue problem for quasi-linear elliptic partial differential equations, Bull. Amer. Math. Soc. 71, (1965) pp. 171-5. | MR 179458 | Zbl 0125.33602

2 M. Berger, An eigenvalue problem for non-linear elliptic partial equations, Trans. Amer. Math. Soc. 120 (1965) pp. 145-184. | MR 181821 | Zbl 0142.08402

3 M. Berger, A Sturm-Liouville theorem for non-linear elliptic partial differential equations, Proc. Nat. Acad. Sci. USA 53, (1965) pp. 1277-9. | MR 188605 | Zbl 0173.43504

4 M. Berger, Ordicx spaces and non-linear, elliptic eigenvalue problems, Bull. Amer. Math. Soc. 79 (1965) pp. 898-902. | MR 185283 | Zbl 0133.05301

5 F. Browder, Variational methods for non-linear elliptic eigenvalue problems, Bull. Amer. Math. Soc. 71 (1965) pp. 176-183. | MR 179459 | Zbl 0135.15802

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 | MR 178248 | Zbl 0136.12003

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). | MR 83702

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 Press 1964, pp. 99-153. | MR 161113 | Zbl 0123.29603

9 L. El'Sgolc, Qualitative Mothods in Mathematical analysis, Vol. 12, Trans. of Math. Monographs A. M. S. 1964. | MR 170048 | Zbl 0476.49001

10 I. Kolodner, Heavy Rotating String-A Non-dinear EigenvaLue Problem. Commun. Pure and Appl. Math. (1955) pp. 395-408. | MR 71605 | Zbl 0065.17202

11 M. Krasnoselsky, Topological Methods in the theory of non-linear integral equations GITTL, Moscow 1956, English trans. Macmillan, New York 1964.

12 M. Krasnoselsky, Positive Solutions of Operator Equations, Noordhoff, Groningen 1964.

13 O. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1963. | MR 155093 | Zbl 0121.42701

14 N. Levinson, Positive eigenfunctions for Au + λ f (u) = 0, Arch. RAt. Mech. Anal. 11 (1962) pp. 258-72. | Zbl 0108.28902

15 J. Leray and J. Lions, Quelques resultats de Vishik. Bull. Soc. Math. France 93,1965(97-107). | Numdam | MR 194733 | Zbl 0132.10502

16 J. Lions, Problemes aux limit dans les equations aux deriveee partielles, Lecture Notes 1962. Universite de Montreal. | MR 251372

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. | JFM 64.0439.01

19 A. Messiah, Quantum Mechanice Vol. II, North Holland. Amsterdam 1962. | Zbl 0102.42602

20 Z. Nehari, Characteristic values associated with a class of non-linear differential equations, Acta Math. 105 (1961) pp. 141-75. | MR 123775 | Zbl 0099.29104

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. | MR 166639 | Zbl 0123.31802

22 L. Schnirelmann, Uber eine neue Kombinatoriske Invariante Monatsh. Math. 37 1930 (131-4). | JFM 56.1134.01

23 J. Schwartz, Seneralizing the Ljusternik-Schnirelmann theory of critical points, Comm. Pure Appl. Math. 17 (1964) pp. 807-15. | MR 144212 | Zbl 0152.40801

24 M. Vainberg, Variational Methods for the investigation of non-linear operators GITTL, Moscow 1959. Engl. trans. Holden Day San Francisco 1964.

25 M. Vishik, Quasilinear Strongly Elliptic Systems of Differential Equations in Divergence Form Trudy Mosk. Math. Obsc. 12 1968 pp. 125-184. | Zbl 0144.36201

26 A. Wilansky, Functional Analysis, Blaisdell, New York 1964. | MR 170186 | Zbl 0136.10603

27 N. Meyers and J. Serrin, [to be published].

28 D. Cole, Transition in circular Couette flow Journal of Fluid Mechanics 21, 1965, pp. 385-425. | Zbl 0134.21705

29 W. Velte, Stäbilitatsverhalten und Verzweigung stationer Lösungen der Navier-Stokasschera Gteichungen, Arch. Rat. Mech. Analy. 17 pp. 97-125 (1964). | MR 182240 | Zbl 0131.41808

30 Yamabe, On a Deformation af Riemannian Structures on Conipact Manifolds, Osaka Math. Jour. 12 (1960), 21-37. | MR 125546 | Zbl 0096.37201

31 H. Bethe, Intermediate Quantum Mechanincs, Benjamin 1964 New York. | MR 161579