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The existence of mulitple solutions of elliptic differential equations


Author: Jane Cronin
Journal: Trans. Amer. Math. Soc. 68 (1950), 105-131
MSC: Primary 36.0X
DOI: https://doi.org/10.1090/S0002-9947-1950-0032891-3
MathSciNet review: 0032891
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  • [1] P. Alexandroff and H. Hopf, Topologie I, Berlin, 1935.
  • [2] J. Cronin, Branch points of solutions of equations in Banach space, Submitted to Trans. Amer. Math. Soc. MR 0040578 (12:716b)
  • [3] -Encyklopädie der Mathematischen Wissenschaften, II, 3.2.
  • [4] T. H. Hildebrandt and L. M. Graves, Implicit functions and their differentials in general analysis, Trans. Amer. Math. Soc. vol. 29 (1927) pp. 127-153. MR 1501380
  • [5] R. Iglisch, Reelle Lösungsfelder der elliptischen Differentialgleichungen $ \Delta u = F(u)$ und nichtlinearer Integralgleichungen, Math. Ann. vol. 101 (1927) pp. 98-119. MR 1512518
  • [6] -, Zur Theorie der reellen Verzweigungen von Lösungen nichtlinearer Integralgleichungen, J. Reine Angew. Math. vol. 164 (1931) pp. 151-172.
  • [7] J. Leray, Note, Topologie des éspaces abstracts de M. Banach, C. R. Acad. Sci. Paris vol. 200 (1935) pp. 1082-1084.
  • [8] J. Leray and J. Schauder, Topologie et équations functionnelles, Ann. École Norm. vol. 51 (1934) pp. 45-78. MR 1509338
  • [9] L. Lichtenstein, Untersuchungen über zweidimensionale reguläre Variationsprobleme I, Monatshefte für Mathematik und Physik vol. 28 (1917) pp. 3-51. MR 1548893
  • [10] C. C. MacDuffee, Vectors and matrices, Carus Mathematical Monograph, No. 7, Mathematical Association of America, 1943. MR 0008595 (5:30i)
  • [11] F. Riesz, Über lineare Funktionalgleichungen, Acta Math. vol. 41 (1918) pp. 71-98. MR 1555146
  • [12] E. H. Rothe, Topological proofs of uniqueness theorems in the theory of differential and integral equations, Bull. Amer. Math. Soc. vol. 45 (1939) pp. 606-613. MR 0000093 (1:18a)
  • [13] J. Schauder, Über den Zusammenhang zwischen der Eindeutigkeit und Lösbarkeit partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Math. Ann. vol. 106 (1932) pp. 661-721. MR 1512780
  • [14] -, Über lineare elliptische Differentialgleichungen zweiter Ordnung, Math. Zeit. vol. 38 (1933-1934) pp. 257-282.
  • [15] E. Schmidt, Zur Theorie der linearen und nichtlinearen Integralgleichungen, Math. Ann. vol. 65 (1907-1908) pp. 370-399. MR 1511472

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DOI: https://doi.org/10.1090/S0002-9947-1950-0032891-3
Article copyright: © Copyright 1950 American Mathematical Society

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