A Sturm-Liouville theorem for nonlinear elliptic partial differential equations
Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Serie 3, Volume 20 (1966) no. 3, pp. 543-582.
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     author = {Berger, Melvyn S.},
     title = {A {Sturm-Liouville} theorem for nonlinear elliptic partial differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche},
     pages = {543--582},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 20},
     number = {3},
     year = {1966},
     mrnumber = {211299},
     zbl = {0147.09503},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1966_3_20_3_543_0/}
}
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Berger, Melvyn S. A Sturm-Liouville theorem for nonlinear elliptic partial differential equations. Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Serie 3, Volume 20 (1966) no. 3, pp. 543-582. http://archive.numdam.org/item/ASNSP_1966_3_20_3_543_0/

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

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

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 | Zbl

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

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

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 | Zbl

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

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 | Zbl

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

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

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 | Zbl

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

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

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

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

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

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

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 | Zbl

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

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

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

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

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

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

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

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