Surjectivity results for nonlinear mappings without oddness conditions

W. Feng; Jeffrey Ronald Leslie Webb

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 15-28
  • ISSN: 0010-2628

Abstract

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Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form λ T ( x ) - S ( x ) = f , where T is invertible, and T , S satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuč’ık, Nečas, Souček, and Souček. We employ the concept of an a -stably-solvable operator, related to nonlinear spectral theory methodology. Applications are given to a nonlinear Sturm-Liouville problem and a three point boundary value problem recently studied by Gupta, Ntouyas and Tsamatos.

How to cite

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Feng, W., and Webb, Jeffrey Ronald Leslie. "Surjectivity results for nonlinear mappings without oddness conditions." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 15-28. <http://eudml.org/doc/248059>.

@article{Feng1997,
abstract = {Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form $\{\lambda \} T(x)-S(x)=f$, where $T$ is invertible, and $T,S$ satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuč’ık, Nečas, Souček, and Souček. We employ the concept of an $a$-stably-solvable operator, related to nonlinear spectral theory methodology. Applications are given to a nonlinear Sturm-Liouville problem and a three point boundary value problem recently studied by Gupta, Ntouyas and Tsamatos.},
author = {Feng, W., Webb, Jeffrey Ronald Leslie},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$(K, L, a)$ homeomorphism; $a$-homogeneous operator; $a$-stably solvable map; homeomorphism; -homogeneous operator; -stably solvable map},
language = {eng},
number = {1},
pages = {15-28},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Surjectivity results for nonlinear mappings without oddness conditions},
url = {http://eudml.org/doc/248059},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Feng, W.
AU - Webb, Jeffrey Ronald Leslie
TI - Surjectivity results for nonlinear mappings without oddness conditions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 15
EP - 28
AB - Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form ${\lambda } T(x)-S(x)=f$, where $T$ is invertible, and $T,S$ satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuč’ık, Nečas, Souček, and Souček. We employ the concept of an $a$-stably-solvable operator, related to nonlinear spectral theory methodology. Applications are given to a nonlinear Sturm-Liouville problem and a three point boundary value problem recently studied by Gupta, Ntouyas and Tsamatos.
LA - eng
KW - $(K, L, a)$ homeomorphism; $a$-homogeneous operator; $a$-stably solvable map; homeomorphism; -homogeneous operator; -stably solvable map
UR - http://eudml.org/doc/248059
ER -

References

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  1. Fučík S., Nečas J., Souček J., Souček V., Spectral Analysis of Nonlinear Operators, Lecture Notes in Mathematics 346, Springer-Verlag, Berlin, Heidelberg, New York, 1973. MR0467421
  2. Furi M., Martelli M., Vignoli A., Contributions to the spectral theory for nonlinear operators in Banach spaces, Ann. Mat. Pura. Appl. (IV) 118 (1978), 229-294. (1978) Zbl0409.47043MR0533609
  3. Webb J.R.L., On degree theory for multivalued mappings and applications, Boll. Un. Mat. It. (4) 9 (1974), 137-158. (1974) Zbl0293.47021MR0367740
  4. Toland J.F., Topological Methods for Nonlinear Eigenvalue Problems, Battelle Advanced Studies Centre, Geneva, Mathematics Report No. 77, 1973. 
  5. Deimling K., Nonlinear Functional Analysis, Springer Verlag, Berlin, 1985. Zbl0559.47040MR0787404
  6. Gupta C.P., Ntouyas S.K., Tsamatos P.Ch., On an m -point boundary-value problem for second-order ordinary differential equations, Nonlinear Analysis, Theory, Methods {&} Applications 23 (1994), 1427-1436. (1994) Zbl0815.34012MR1306681
  7. Gupta C.P., Ntouyas S.K., Tsamatos P.Ch., Solvability of an m -point boundary value problem for second order ordinary differential equations, J. Math. Anal. Appl. 189 (1995), 575-584. (1995) Zbl0819.34012MR1312062
  8. Gupta C.P., A note on a second order three-point boundary value problem, J. Math. Anal. Appl. 186 (1994), 277-281. (1994) Zbl0805.34017MR1290657

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