Fredholm alternatives and surjectivity results for multivalued $A$-proper and condensing mappings with applications to nonlinear integral and differential equations

Milojević, Petronije S.

Czechoslovak Mathematical Journal, Tome 30 (1980) no. 3, pp. 387-417

Détail

DOI : 10.21136/CMJ.1980.101690

Classification : 34B15, 35G30, 45G05, 47H09

Bibliographie

[1] F. E. Browder: Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc. Sympos. Pure Math. vol. 18, II, 1976. | MR | Zbl

[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

[3] Ch. Castaing: Sur les multi-applications mesurables. Revue Inf. Rech. Op. 1 (1967), 91-126. | MR | Zbl

[4] S. Fučík: Note on the Fredholm alternative for nonlinear operators. Comment. Math. Univ. Carolinae, 12 (1971), 213-226. | MR

[5] S. Fučík: Nonlinear equations with noninvertible linear part. Czech. Math. J. 24 (1974), 467-497. | MR

[6] S. Fučík: Ranges of nonlinear operators. Vol. I-V, Lectures Notes, Charles University, Prague, 1976/77.

[7] S. Fučík M. Kučera, J. Nečas: Ranges of nonlinear asymptotically linear operators. J. Diff. Equations 17 (1975), 375-394. | DOI | MR

[8] A. Granas: The theory of compact vector fields. Rozprawy Matematyczne, 1962. | Zbl

[9] P. Hess: On the Fredholm alternative for nonlinear functional equations in Banach spaces. Proc. Amer. Math. Soc., 33 (1972), 55-61. | DOI | MR | Zbl

[10] S. Hildebrandt, E. Wienholtz: Constructive proofs of representation theorems in separable Hilbert spaces. Comm. Pure and Appl. Math. 17 (1964), 369-373. | DOI | MR

[11] R. I. Kachurovsky: On Fredholm theory for nonlinear operator equations. Dokl. Akad. Nauk SSSR, 192 (1970), 751-754.

[12] R. I. Kachurovsky: On linear operators whose ranges are subspaces. Dokl. Akad. Nauk SSSR, 196 (1971), 168-172.

[13] T. Kato: Perturbation theory for nullity difficiency and other quantities of linear operators. J. Analyse Math. 6 (1958), 273-322. | DOI | MR

[14] C. Kuratowski: Sur les espaces complets. Fund. Math. 15 (1930), 301-309. | DOI

[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. | MR | Zbl

[16] T. W. Ma: Topological degrees for set-valued compact vector fields in locally convex spaces. Dissertations Math. 92 (1972), 1-43. | MR

[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.

[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

[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. | DOI | MR

[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

[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.

[22] P. S. Milojevič: Fixed point theorems for multivalued approximable mappings. Proc. Amer. Math. Soc. 73 (1) (1979), 65-72. | DOI | MR

[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. | DOI | MR

[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. | DOI | MR

[25] G. J. Minty: Monotone (nonlinear) operators in Hilbert spaces. Duke Math. J. 29 (1962), 341-346. | DOI | MR

[26] R. D. Nussbaum: The radius of the essential spectrum. Duke Math. J. 38 (1970), 473--478. | MR | Zbl

[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. | DOI | MR

[28] W. V. Petryshyn: Remarks on condensing and $k$-set-contractive mappings. J. Math. Anal. Appl. 39 (3) (1972), 717-741. | DOI | MR | Zbl

[29] W. V. Petryshyn: Fredholm alternative for nonlinear $k$-ball contractive mappings with applications. J. Difif. Equat. 17 (1975), 82-95. | DOI | MR | Zbl

[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. | DOI | MR

[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. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[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. | DOI | MR

[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

[35] В. N. Sadovskii: Ultimately compact and condensing mappings. Uspehi Mat. Nauk, 27 (1972), 81-146. | MR

[36] С. A. Stuart: Some bifurcation theory for $k$-set contractions. Proc. London Math. Soc. (3) 27 (1973), 531-550. | MR | Zbl

[37] J. F. Toland: Global bifurcation theory via Galerkin method. J. Nonlinear Anal., Theory, Methods, Appl. 1 (3) (1977), 305-317. | MR

[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. | MR | Zbl

[39] J. R. L. Webb: On a characterization of $k$-set contractions. Accad. Naz. Lincei. 8 (1971), 358-361. | MR

[40] J. R. L. Webb: On degree theory for multivalued mappings and applications. Bulletino Un. Mat. Ital. (4) 9 (1974), 137-158. | MR | Zbl

[41] F. Wille: On motone operators with perturbations. Arch. Rational Mech. Anal. 46 (1972), 269-388.