| Title:
|
Equations with discontinuous nonlinear semimonotone operators (English) |
| Author:
|
Buong, Nguyen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
7-12 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type $x+KF(x)=0$ with the discontinuous semimonotone operator $F$. Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in $L_p(\Omega )$ are given for illustration. (English) |
| Keyword:
|
semimonotone operators |
| Keyword:
|
uniformly convex Banach spaces |
| MSC:
|
45G10 |
| MSC:
|
45N05 |
| MSC:
|
47H15 |
| MSC:
|
47H30 |
| MSC:
|
47J05 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1060.47509 |
| idMR:
|
MR1715199 |
| . |
| Date available:
|
2009-01-08T18:49:21Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119060 |
| . |
| Reference:
|
[1] Amann H.: Ein Existenz und Eindeutigkeitssatz fur die Hammersteinshe Gleichung in Banachraumen.Math. Z. 111 (1969), 175-190. MR 0254687 |
| Reference:
|
[2] Amann H.: Uber die naherungsweise Losung nichlinearer Integralgleichungen.Numer. Math. 19 (1972), 29-45. MR 0303772 |
| Reference:
|
[3] Brezis H., Browder F.: Nonlinear integral equations and systems of Hammerstein's type.Adv. Math. 10 (1975), 115-144. MR 0394341 |
| Reference:
|
[4] Brezis H., Sibony M.: Méthod d'approximation et d'itération pour les opérateurs monotones.Arch. Rat. Mech. Anal. 28 (1968), 1 59-82. MR 0220110 |
| Reference:
|
[5] Buong N.: On solution of the operator equation of Hammerstein type with semimonotone and discontinuous nonlinearity (in Vietnamese).J. Math. 12 (1984), 25-28. |
| Reference:
|
[6] Buong N.: On approximate solutions of Hammerstein equation in Banach spaces (in Russian).Ukrainian Math. J. 8 (1985), 1256-1260. |
| Reference:
|
[7] Gaidarov D.P., Raguimkhanov P.K.: On integral inclusion of Hammerstein (in Russian).Sibirian Math. J. 21 (1980), 2 19-24. MR 0569173 |
| Reference:
|
[8] Ganesh M., Joshi M.: Numerical solvability of Hammerstein equations of mixed type.IMA J. Numer. Anal. 11 (1991), 21-31. MR 1089546 |
| Reference:
|
[9] Gupta C.P.: Nonlinear equations of Urysohn's type in a Banach space.Comment. Math. Univ. Carolinae 16 (1975), 377-386. Zbl 0326.47058, MR 0500344 |
| Reference:
|
[10] Emellianov C.V.: Systems of Automatic Control with Variable Structure (in Russian).Moscow, Nauka, 1967. |
| Reference:
|
[11] Joshi M.: Existence theorem for a generalized Hammerstein type equation.Comment. Math. Univ. Carolinae 15 (1974), 283-291. Zbl 0291.47034, MR 0348569 |
| Reference:
|
[12] Krasnoselskii A.M.: On elliptic equations with discontinuous nonlinearities (in Russian).Dokl. AN RSPP 342 (1995), 6 731-734. MR 1346871 |
| Reference:
|
[13] Pavlenko V.N.: Nonlinear equations with discontinuous operators in Banach space (in Russian).Ukrainian Math. J. 31 (1979), 5 569-572. MR 0552495 |
| Reference:
|
[14] Pavlenko V.N.: Existence of solution for nonlinear equations involving discontinuous semimonotone operators (in Russian).Ukrainian Math. J. 33 (1981), 4 547-551. |
| Reference:
|
[15] Raguimkhanov: Concerning an existence problem for solution of Hammerstein equation with discontinuous mappings (in Russian).Izvestia Vukov, Math. (1975), 10 62-70. |
| Reference:
|
[16] Vaclav D.: Monotone Operators and Applications in Control and Network Theory.Elsevier, Amsterdam-Oxford-New York, 1979. Zbl 0425.93002, MR 0554232 |
| Reference:
|
[17] Vainberg M.M.: Variational Method and Method of Monotone Operators (in Russian).Moscow, Nauka, 1972. MR 0467427 |
| . |
