| Title:
|
Surjectivity results for nonlinear mappings without oddness conditions (English) |
| Author:
|
Feng, W. |
| Author:
|
Webb, J. R. L. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
15-28 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 Fu\v{c}'{\i}k, Ne\v{c}as, Sou\v{c}ek, and Sou\v{c}ek. 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. (English) |
| Keyword:
|
$(K, L, a)$ homeomorphism |
| Keyword:
|
$a$-homogeneous operator |
| Keyword:
|
$a$-stably solvable map |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
47H12 |
| MSC:
|
47H15 |
| MSC:
|
47J05 |
| MSC:
|
47J10 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0886.47034 |
| idMR:
|
MR1455467 |
| . |
| Date available:
|
2009-01-08T18:28:51Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118899 |
| . |
| Reference:
|
[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. MR 0467421 |
| Reference:
|
[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. Zbl 0409.47043, MR 0533609 |
| Reference:
|
[3] Webb J.R.L.: On degree theory for multivalued mappings and applications.Boll. Un. Mat. It. (4) 9 (1974), 137-158. Zbl 0293.47021, MR 0367740 |
| Reference:
|
[4] Toland J.F.: Topological Methods for Nonlinear Eigenvalue Problems.Battelle Advanced Studies Centre, Geneva, Mathematics Report No. 77, 1973. |
| Reference:
|
[5] Deimling K.: Nonlinear Functional Analysis.Springer Verlag, Berlin, 1985. Zbl 0559.47040, MR 0787404 |
| Reference:
|
[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. Zbl 0815.34012, MR 1306681 |
| Reference:
|
[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. Zbl 0819.34012, MR 1312062 |
| Reference:
|
[8] Gupta C.P.: A note on a second order three-point boundary value problem.J. Math. Anal. Appl. 186 (1994), 277-281. Zbl 0805.34017, MR 1290657 |
| . |
