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A comparison theorem for eigenfunctions


Author: C. A. Swanson
Journal: Proc. Amer. Math. Soc. 37 (1973), 537-540
MSC: Primary 35B05
DOI: https://doi.org/10.1090/S0002-9939-1973-0312041-7
MathSciNet review: 0312041
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Abstract: A comparison theorem of Sturm's type is obtained for eigenfunctions of general linear elliptic partial differential operators of second order on bounded domains of n-dimensional Euclidean space. The proof is almost immediate from an earlier identity of the author. The theorem is shown to be stronger than some recent theorems of Kurt Kreith.


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  • [1] W. Allegretto, A comparison theorem for nonlinear operators, Ann. Scuola Norm. Sup. Pisa (3) 25 (1971), 41-46. MR 0298181 (45:7233)
  • [2] D. R. Dunninger and R. J. Weinacht, Separation and comparison theorems for classes of singular elliptic inequalities and degenerate elliptic inequalities, Applicable Anal. 1 (1971), 43-55. MR 0289922 (44:7107)
  • [3] K. Kreith, A comparison theorem for general elliptic equations with mixed boundary conditions, J. Differential Equations 8 (1970), 537-541. MR 42 #646. MR 0265737 (42:646)
  • [4] -, A class of comparison theorems for nonselfadjoint elliptic equations, Proc. Amer. Math. Soc. 29 (1971), 547-552. MR 0279418 (43:5140)
  • [5] C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611-616. MR 34 #1663. MR 0201781 (34:1663)
  • [6] -, A generalization of Sturm's comparison theorem, J. Math. Anal. Appl. 15 (1966), 512-519. MR 34 #4656. MR 0204820 (34:4656)
  • [7] -, An identity for elliptic equations with applications, Trans. Amer. Math. Soc. 134 (1968), 325-333. MR 38 #400. MR 0232074 (38:400)
  • [8] -, Comparison theorems for elliptic differential systems, Pacific J. Math. 33 (1970), 445-450. MR 41 #7255. MR 0262650 (41:7255)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0312041-7
Keywords: Nonselfadjoint elliptic equation, Sturmian comparison theorem, homogeneous boundary condition, Green formula
Article copyright: © Copyright 1973 American Mathematical Society

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