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Applicable Analysis
An International Journal
Volume 1, 1971 - Issue 1
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Miscellany

Separation and comparison theorems for classes of singular elliptic inequalities and degenerate elliptic inequalities

D. R. Dunninger Rensselaer Polytechnic Institute, Troy, New York
&
R. J. Weinacht University of Delaware, Newark, Delaware; Rensselaer Polytechnic Institute, Troy, New York
Pages 43-55 | Published online: 04 Mar 2011

References

  • Allegretto , W. 1970 . A generalization of Sturm's separation theorem . Proc. Amer. Math Soc , 25 : 151 – 154 .
  • Clark , C. and Swanson , C. A. 1965 . Comparison theorems for elliptic differential equations . Proc. Amer. Math. Soc , 16 : 886 – 890 .
  • Diaz , J. B. and Mclaughlin , J. R. 1969 . Sturm separation and comparison theorems for ordinary and partial differential equations . Atti Accad. Naz. Lincei Mem , 9 : 134 – 194 .
  • Dunninger , D. R. 1970 . A Picone identity for non-self-adjoint elliptic operators . Atti Accad.Naz. Lincei Rend , 48 : 133 – 139 .
  • Gantmacher , F. R. 1959 . The Theory of Matrices , Vol. 1 , New York : Chelsea .
  • Gilbert , R. P. 1969 . Function Theoretic Methods in Partial Differential Equations , New York and London : Academic Press .
  • Hormander , L. 1963 . Linear Partial Differential Operators , Berlin : Springer-Verlag .
  • Kellogg , O. D. 1929 . Foundations of Potential Theory , New York : Frederick Ungar Publishing Co .
  • Kreith , K. 1968 . A generalized Picone identity . Atti Accad. Naz. Lincei Rend , 45 : 217 – 220 .
  • Leighton , W. 1962 . Comparison theorems for linear differential equations of second order . Proc. Amer. Math. Soc , 13 : 603 – 610 .
  • Picone , M. 1911 . Un teorema sulle soluzioni delle equazioni lineari ellitiche autoaggiunte alle derivate parziali del secondo-ordine . Atti Accad. Naz. Lincei Rend , 20 : 213 – 219 .
  • Protter , M. H. and Weinberger , H. F. 1967 . Maximum Principles in Differential Equations , N. J : Prentice-Hall .
  • Swanson , C. A. 1968 . Comparison and Oscillation Theory of Linear Differential Equations , New York and London : Academic Press .
  • Visik , M. I. 1954 . Boundary value problems for elliptic equations degenerating on the boundary of the region . Mat. Sb , 35 : 513 – 568 .
  • Weinstein , A. 1948 . Discontinuous integrals and generalized potential theory . Trans. Amer.Math. Soc. , 63 : 342 – 354 .
  • Weinstein , A. 1953 . Generalized axially symmetric potential theory . Bull. Amer. Math.Soc. , 59 : 20 – 38 .
  • Weinstein , A. 1962 . Fluid Dynamics and Applied Mathematics , 29 – 49 . New York : Gordon and Breach .

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