Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Sturm comparison theorems for elliptic inequalities


Authors: W. Allegretto and C. A. Swanson
Journal: Bull. Amer. Math. Soc. 75 (1969), 1318-1321
DOI: https://doi.org/10.1090/S0002-9904-1969-12411-0
MathSciNet review: 0245959
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. W. Allegretto, Comparison and osculation theorems for elliptic equations, Ph.D. thesis, University of British Columbia, Vancouver, British Columbia, Canada, 1969.
  • 2. Colin Clark and C. A. Swanson, Comparison theorems for elliptic differential equations, Proc. Amer. Math. Soc. 16 (1965), 886-890. MR 180753
  • 3. J. B. Diaz and Joyce R. McLaughlin, Sturm comparison theorems for ordinary and partial differential equations, Bull. Amer. Math. Soc. 75 (1969), 335-339. MR 239244
  • 4. Philip Hartman and Aurel Wintner, On a comparison theorem for self-adjoint partial differential equations of elliptic type, Proc. Amer, Math. Soc. 6 (1955), 862-865. MR 74668
  • 5. V. B. Headley and C. A. Swanson, Oscillation criteria for elliptic equations Pacific J. Math. 27 (1968), 501-506. MR 236502
  • 6. Kurt Kreith, A new proof of a comparison theorem for elliptic equations, Proc Amer. Math. Soc. 14 (1963), 33-35. MR 149067
  • 7. Kurt Kreith, Comparison theorems for constrained rods, SIAM Rev 6 (1964), 31-36. MR 160963
  • 8. Kurt Kreith, A strong comparison theorem for selfadjoint elliptic equations, Proc Amer. Math. Soc. 19 (1968), 989-990. MR 227594
  • 9. Kurt Kreith, A remark on a comparison theorem of Swanson, Proc. Amer. Math. Soc 20 (1969), 549-550. MR 236503
  • 10. L. M. Kuks, Sturm's theorem and oscillation of solutions of strongly elliptic systems, Soviet Math. Dokl. 3 (1962), 24-27.
  • 11. A. McNabb, Strong comparison theorems for elliptic equations of second order, J. Math. Mech. 10 (1961), 431-440. MR 142881
  • 12. Mauro Picone, Un teorema sulle soluzioni delle equazioni lineari ellittiche autoaggiunte alle derivate parziali del secondo-ordine, Rend. Ace. Lincei 20 (1) (1911), 213-219.
  • 13. M. H. Protter, A comparison theorem for elliptic equations, Proc. Amer. Math. Soc. 10 (1959), 296-299. MR 107076
  • 14. R. M. Redheffer, A Sturmian theorem for partial differential equations, Proc. Amer. Math. Soc. 8 (1957), 458-462. MR 86253
  • 15. C. A. Swanson, A generalization of Sturm's comparison theorem, J. Math. Anal. Appl. 15 (1966), 512-519. MR 204820
  • 16. C. A. Swanson, Comparison theorems for elliptic equations on unbounded domains, Trans. Amer. Math. Soc. 126 (1967), 278-285. MR 203211
  • 17. C. A. Swanson, An identity for elliptic equations with applications, Trans. Amer. Math. Soc. 134 (1968), 325-333. MR 232074
  • 18. C. A. Swanson, Comparison and oscillation theory of linear differential equations, Mathematics in Science and Engineering, vol. 48, Academic Press, New York, 1968. MR 463570
  • 19. C. A. Swanson, Comparison theorems for quasilinear elliptic differential inequalities, J. Differential Equations (to appear). MR 255968


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1969-12411-0

American Mathematical Society