| Title:
|
Fredholm alternatives and surjectivity results for multivalued $A$-proper and condensing mappings with applications to nonlinear integral and differential equations (English) |
| Author:
|
Milojević, Petronije S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1980 |
| Pages:
|
387-417 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34B15 |
| MSC:
|
35G30 |
| MSC:
|
45G05 |
| MSC:
|
47H09 |
| idZBL:
|
Zbl 0467.47039 |
| idMR:
|
MR583620 |
| DOI:
|
10.21136/CMJ.1980.101690 |
| . |
| Date available:
|
2008-06-09T14:40:06Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101690 |
| . |
| Reference:
|
[1] F. E. Browder: Nonlinear operators and nonlinear equations of evolution in Banach spaces.Proc. Sympos. Pure Math. vol. 18, II, 1976. Zbl 0327.47022, MR 0405188 |
| Reference:
|
[2] F. E. Browder: Existence theory for boundary value problems for quasilinear elliptic systems with strong nonlinear lower order terms.in "Proceedings Symp. Pure Math." Vol. 23, pp. 269-286, Amer. Math. Soc., Providence, R.I., 1973. MR 0340815 |
| Reference:
|
[3] Ch. Castaing: Sur les multi-applications mesurables.Revue Inf. Rech. Op. 1 (1967), 91-126. Zbl 0153.08501, MR 0223527 |
| Reference:
|
[4] S. Fučík: Note on the Fredholm alternative for nonlinear operators.Comment. Math. Univ. Carolinae, 12 (1971), 213-226. MR 0288641 |
| Reference:
|
[5] S. Fučík: Nonlinear equations with noninvertible linear part.Czech. Math. J. 24 (1974), 467-497. MR 0348568 |
| Reference:
|
[6] S. Fučík: Ranges of nonlinear operators.Vol. I-V, Lectures Notes, Charles University, Prague, 1976/77. |
| Reference:
|
[7] S. Fučík M. Kučera, J. Nečas: Ranges of nonlinear asymptotically linear operators.J. Diff. Equations 17 (1975), 375-394. MR 0372696, 10.1016/0022-0396(75)90050-9 |
| Reference:
|
[8] A. Granas: The theory of compact vector fields.Rozprawy Matematyczne, 1962. Zbl 0111.11001 |
| Reference:
|
[9] P. Hess: On the Fredholm alternative for nonlinear functional equations in Banach spaces.Proc. Amer. Math. Soc., 33 (1972), 55-61. Zbl 0249.47064, MR 0301585, 10.1090/S0002-9939-1972-0301585-9 |
| Reference:
|
[10] S. Hildebrandt, E. Wienholtz: Constructive proofs of representation theorems in separable Hilbert spaces.Comm. Pure and Appl. Math. 17 (1964), 369-373. MR 0166608, 10.1002/cpa.3160170309 |
| Reference:
|
[11] R. I. Kachurovsky: On Fredholm theory for nonlinear operator equations.Dokl. Akad. Nauk SSSR, 192 (1970), 751-754. |
| Reference:
|
[12] R. I. Kachurovsky: On linear operators whose ranges are subspaces.Dokl. Akad. Nauk SSSR, 196 (1971), 168-172. |
| Reference:
|
[13] T. Kato: Perturbation theory for nullity difficiency and other quantities of linear operators.J. Analyse Math. 6 (1958), 273-322. MR 0107819, 10.1007/BF02790238 |
| Reference:
|
[14] C. Kuratowski: Sur les espaces complets.Fund. Math. 15 (1930), 301-309. 10.4064/fm-15-1-301-309 |
| Reference:
|
[15] A. Lasota, Z. Opial: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations.Bull. Acad. Pol. Sci., Ser. Sci. Math., astr. et phys. 13 (1965), 781-786. Zbl 0151.10703, MR 0196178 |
| Reference:
|
[16] T. W. Ma: Topological degrees for set-valued compact vector fields in locally convex spaces.Dissertations Math. 92 (1972), 1-43. MR 0309103 |
| Reference:
|
[17] P. S. Milojevič: Multivalued mappings of $A$-proper and condensing type and boundary value problems.Ph. D. Thesis, Rutgers University, New Brunswick, N. J., May 1975. |
| Reference:
|
[18] P. S. Milojevič: Some generalizations of the first Fredholm theorem to multivalued condensing and $A$-proper mappings.Bulletino Un. Math. Ital. (5) 13-B (1976), 619-633. MR 0435964 |
| Reference:
|
[19] P. S. Milojevič: A generalization of Leray-Schauder theorem and surjectivity results for multivalued $A$-proper and pseudo $A$-proper mappings.J. Nonlinear Anal., Theory, Methods and Appl. 1 (3) (1977), 263-276. MR 0637079, 10.1016/0362-546X(77)90035-9 |
| Reference:
|
[20] P. S. Milojevič: Some generalizations of the first Fredholm theorem to multivalued $A$-proper mappings with applications to nonlinear elliptic equations.J. Math. Anal. Appl. 65 (2) (1978). MR 0506319 |
| Reference:
|
[21] P. S. Milojevič: On the solvability and continuation type results for nonlinear equations with applications I.Proc. Third Inter. Symp. on Top. and Applic., Belgrade, 1977, 468 to 502. |
| Reference:
|
[22] P. S. Milojevič: Fixed point theorems for multivalued approximable mappings.Proc. Amer. Math. Soc. 73 (1) (1979), 65-72. MR 0512060, 10.1090/S0002-9939-1979-0512060-7 |
| Reference:
|
[23] P. S. Milojevič, W. V. Petryshyn: Continuation theorems and the approximation - solvability of equations involving multivalued $A$-ргорег mappings.J. Math. Anal. Appl. 60 (3) (1977), 658-692. MR 0454760, 10.1016/0022-247X(77)90007-5 |
| Reference:
|
[24] P. S. Milojevič, W. V. Petryshyn: Continuation and surjectivity theorems for uniform limits of $А$-рrореr mappings with applications.J. Math. Anal. Appl. 62 (1978), 368-400. MR 0482432, 10.1016/0022-247X(78)90134-8 |
| Reference:
|
[25] G. J. Minty: Monotone (nonlinear) operators in Hilbert spaces.Duke Math. J. 29 (1962), 341-346. MR 0169064, 10.1215/S0012-7094-62-02933-2 |
| Reference:
|
[26] R. D. Nussbaum: The radius of the essential spectrum.Duke Math. J. 38 (1970), 473--478. Zbl 0216.41602, MR 0264434 |
| Reference:
|
[27] W. V. Petryshyn: On projectional-solvability and the Fredholm alternative for equations involving linear $A$-ргорег operators.Arch. Rat. Mech. Anal. 30 (1968), 270-284. MR 0231221, 10.1007/BF00281535 |
| Reference:
|
[28] W. V. Petryshyn: Remarks on condensing and $k$-set-contractive mappings.J. Math. Anal. Appl. 39 (3) (1972), 717-741. Zbl 0238.47041, MR 0328687, 10.1016/0022-247X(72)90194-1 |
| Reference:
|
[29] W. V. Petryshyn: Fredholm alternative for nonlinear $k$-ball contractive mappings with applications.J. Difif. Equat. 17 (1975), 82-95. Zbl 0292.47057, MR 0355713, 10.1016/0022-0396(75)90036-4 |
| Reference:
|
[30] W. V. Petryshyn: Fredholm alternative for nonlinear $A$-ргорег mappings with applications to nonlinear elliptic value problems.J. Funct. Anal. 18 (1975), 288-317. MR 0361963, 10.1016/0022-1236(75)90018-X |
| Reference:
|
[31] W. V. Petryshyn: On the approximation-solvability of equations involving $A$-proper and pseudo $A$-proper mappings.Bull. Amer. Math. Soc. 81 (2) (1975), 223-312. Zbl 0303.47038, MR 0388173, 10.1090/S0002-9904-1975-13728-1 |
| Reference:
|
[32] W. V. Petryshyn: Note on the solvability of equations involving unbounded linear and quasibounded nonlinear operators.J. Math. Anal. Appl. 56 (1976), 495-501. Zbl 0352.47029, MR 0430888, 10.1016/0022-247X(76)90021-4 |
| Reference:
|
[33] W. V. Petryshyn, P. M. Fitzpatrick: A degree theory, fixed point theorems and mapping theorems for multivalued and noncompact mappings.Trans. Amer. Math. Soc. 194 (1974), 1-25. MR 2478129, 10.1090/S0002-9947-1974-2478129-5 |
| Reference:
|
[34] W. V. Petryshyn, P. M. Fitzpatrick: On 1-set and -ball contractions with application to perturbation problems for nonlinear bijective maps and linear Fredholm maps.Bulletino Un. Math. Ital. (4) 7 (1973), 102-124. MR 0343114 |
| Reference:
|
[35] В. N. Sadovskii: Ultimately compact and condensing mappings.Uspehi Mat. Nauk, 27 (1972), 81-146. MR 0428132 |
| Reference:
|
[36] С. A. Stuart: Some bifurcation theory for $k$-set contractions.Proc. London Math. Soc. (3) 27 (1973), 531-550. Zbl 0268.47064, MR 0333856 |
| Reference:
|
[37] J. F. Toland: Global bifurcation theory via Galerkin method.J. Nonlinear Anal., Theory, Methods, Appl. 1 (3) (1977), 305-317. MR 0516195 |
| Reference:
|
[38] A. Vignoli: On quasibounded mappings and nonlinear functional equations.Atti Acad. Naz. Lincei Rendi. cl. sci. Fiz. Mat. Natur. (8) 50 (1971), 114-117. Zbl 0254.47089, MR 0303379 |
| Reference:
|
[39] J. R. L. Webb: On a characterization of $k$-set contractions.Accad. Naz. Lincei. 8 (1971), 358-361. MR 0306991 |
| Reference:
|
[40] J. R. L. Webb: On degree theory for multivalued mappings and applications.Bulletino Un. Mat. Ital. (4) 9 (1974), 137-158. Zbl 0293.47021, MR 0367740 |
| Reference:
|
[41] F. Wille: On motone operators with perturbations.Arch. Rational Mech. Anal. 46 (1972), 269-388. |
| . |
