Connected branches of asymptotically equivalent solutions to non-linear eigenvalue problems

Allan L. Edelson; Maria Patrizia Pera

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1987)

  • Volume: 81, Issue: 4, page 337-346
  • ISSN: 1120-6330

Abstract

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We prove an existence theorem for connected branches of solutions to nonlinear operator equations in Banach spaces. This abstract result is applied to the asymptotically equivalent solutions to nonlinear ordinary differential equations.

How to cite

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Edelson, Allan L., and Pera, Maria Patrizia. "Connected branches of asymptotically equivalent solutions to non-linear eigenvalue problems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 81.4 (1987): 337-346. <http://eudml.org/doc/287402>.

@article{Edelson1987,
abstract = {We prove an existence theorem for connected branches of solutions to nonlinear operator equations in Banach spaces. This abstract result is applied to the asymptotically equivalent solutions to nonlinear ordinary differential equations.},
author = {Edelson, Allan L., Pera, Maria Patrizia},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Nonlinear eigenvalue problems; fixed point index; asymptotic equivalence of solutions; connected branches of solutions},
language = {eng},
month = {12},
number = {4},
pages = {337-346},
publisher = {Accademia Nazionale dei Lincei},
title = {Connected branches of asymptotically equivalent solutions to non-linear eigenvalue problems},
url = {http://eudml.org/doc/287402},
volume = {81},
year = {1987},
}

TY - JOUR
AU - Edelson, Allan L.
AU - Pera, Maria Patrizia
TI - Connected branches of asymptotically equivalent solutions to non-linear eigenvalue problems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1987/12//
PB - Accademia Nazionale dei Lincei
VL - 81
IS - 4
SP - 337
EP - 346
AB - We prove an existence theorem for connected branches of solutions to nonlinear operator equations in Banach spaces. This abstract result is applied to the asymptotically equivalent solutions to nonlinear ordinary differential equations.
LA - eng
KW - Nonlinear eigenvalue problems; fixed point index; asymptotic equivalence of solutions; connected branches of solutions
UR - http://eudml.org/doc/287402
ER -

References

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  1. AMANN, H. (1976) - Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, «SIAM Review», 18, 620-709. Zbl0345.47044MR415432
  2. BROWN, R.F. (1971) - The Lefschetz fixed point theorem, Scott, Foresman and Company, Glenview, Illinois. Zbl0216.19601MR283793
  3. DANCER, E.N. (1973) - Global solutions branches for positive maps, «Arch. Rational Mech. Anal.», 52, 181-192. Zbl0275.47043MR353077
  4. EDELSON, A.L. and SCHUUR, J.D. (1983) - Asymptotic and strong asymptotic equivalence to polynomials for solutions of nonlinear differential equations, Proc. Equadiff 82, Wurzburg, «Lecture Notes in Math.», 1017, Springer Verlag, Berlin. Zbl0526.34022
  5. FURI, M. and PERA, M.P. - A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals, to appear in «Annales Polonici Math.». Zbl0656.47052MR927581
  6. GRANAS, A. (1972) - The Leray-Schauder index and the fixed point theory for arbitrary ANR's, «Bull. Soc. Math. France», 100, 209-228. Zbl0236.55004MR309102
  7. KITAMURA, Y. and KUSANO, T. (1980) - Nonlinear oscillation of higher order functional differential equations with deviating arguments, «J. Mathematical Analysis and Appl.», 77, 100-119. Zbl0465.34044MR591264DOI10.1016/0022-247X(80)90263-2
  8. KURATOWSKI, K. (1968) - Topology, vol. 2, Academic Press, New York. 
  9. RABINOWITZ, P.H. (1971) - Some global results for nonlinear eigenvalue problems, «J. Functional Anal.», 7, 487-513. Zbl0212.16504MR301587
  10. WHYBURN, G.T. (1958) - Topological Analysis, Princeton University Press. Zbl0080.15903MR99642

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