Publication Cover
Applicable Analysis
An International Journal
Volume 1, 1971 - Issue 2
13
Views
17
CrossRef citations to date
0
Altmetric
Original Articles

Estimates for the number of solutions of operator equations

Pages 183-200 | Published online: 24 May 2007

References

  • Browder , F. E. 1968 . Topology and non-linear functional equations . Studia Mathematica , 31 : 189 – 204 .
  • Browder , F. E. 1968 . Nonlinear Operators and Nonlinear Equations of Evolution . AMS Proceedings of the Symposium on Nonlinear Functional Analysis , 31 : 189 – 204 .
  • Browder , F. E. and Gupta , C. P. 1969 . Topological degree and nonlinear mappings of analytic type in Banach spaces . Journ. Math. Anal. andApp , 26 : 390 – 402 .
  • Browder , F. E. and Nussbaum , R. D. 1968 . The topological degree for noncompact nonlinear mappings in Banach spaces . Bull. Amer. Math. Soc , 74 : 671 – 676 .
  • Cronin , J. 1953 . Analytic functional mappings . Ann. Math , 58 : 175 – 181 .
  • Cronin , J. 1968 . “ Upper and Lower Bounds for the Number of Solutions of Nonlinear Equations ” . In AMS Proceedings of the Symposium on Nonlinear Functional Analysis Chicago
  • Cronin , J. 1953 . Topological degree and the number of solutions of equations . Duke Math.Jour , 58
  • Elworthy K. D. Tromba A. J. Degree theory on Banach manifolds to appear
  • Elworthy , K. D. 1964 . Fixed Points and Topological Degree in Nonlinear Analysis , Providence, R.I : American Mathematical Society .
  • Lichtenstein , L. 1931 . Vorlesungen ilber einige Klassen nichtlinearen Integralgleichungen und Integro-Differential-gleichungen nebst Anwendungen , Berlin : Springer .
  • Nussbaum , R. D. 1969 . The fixed point index and asymptotic fixed point theorems for k-set-contractions . Bull Amer. Math. Soc , 75 : 490 – 495 .
  • Nussbaum , R. D. 1969 . The fixed point index for local condensing maps . Ann. Mat. Pura Appl , 75
  • Nussbaum , R. D. 1969 . Degree theory for local condensing maps . Jour. Math. Anal. Appl , 75
  • Nussbaum , R. D. 1969 . The Fixed Point Index and Fixed Point Theorems for k-Set-Contractions , University of Chicago .
  • Nussbaum , R. D. 1970 . The radius of the essential spectrum . Duke Math. Jour , 38 : 473 – 478 .
  • Remmert , R. and Stein , K. 1953 . Ober die wesentlichen singularitaten analytischer mengen . Math. Ann , 126 : 263 – 306 .
  • Sard , A. 1942 . The measure of the critical values of differentiable maps . Bull. Amer. Math.Soc , 48 : 883 – 890 .
  • Sard , A. 1965 . Hausdorff measures of critical images on Banach manifolds . Amer. Jour, Math , 87 : 158 – 174 .
  • Schmidt , E. 1907 . Zur theorie der linearen und nicht linearen integralgleichungen . Math. Ann , 65 : 370 – 390 .
  • Schwartz , J. T. 1963 . Compact analytical mappings of B-spaces and a theorem of Jane Cronin . Comm. onPureandApp. Math , 16 : 253 – 260 .
  • Smale , S. 1965 . An infinite dimensional version of Sard's theorem . Amer. Jour. Math , 87 : 861 – 866 .
  • Taylor , A. E. 1966 . Theorems on ascent, descent, nullity and defect of linear operators . Math. Ann , 163 : 18 – 49 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.