Some generalizations of the first Fredholm theorem to multivalued A- proper mappings with applications to nonlinear elliptic equations. (English) Zbl 0389.47029
References:
| [1] | Browder, F. E., Existence theorems for nonlinear partial differential equations, (Proc. Symp. Pure Math. Amer. Math. Soc., 16 (1970)), 1-60 · Zbl 0212.27704 |
| [2] | Browder, F. E.; Petryshyn, W. V., Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces, J. Functional Analysis, 3, 217-245 (1969) · Zbl 0177.42702 |
| [3] | Gohberg, I. T.; Goldenstein, L. S.; Markus, A. S., Investigation of some properties of bounded linear operators in connection with their \(q\)-norms, Ucen. Zap. Kishinevsk Inst., 29, 29-36 (1957) |
| [4] | Granas, A., Theorem on antipodes and theorems on fixed points for a certain class of multivalued mappings in Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 7, 271-275 (1959) · Zbl 0089.11202 |
| [5] | Grigorieff, R. D., Uber die Fredholm-Alternative bei linearen approximations-regularen Operatoren, Applicable Anal., 2, 217-227 (1972) · Zbl 0244.47005 |
| [6] | Hess, P., On the Fredholm alternative for nonlinear functional equations in Banach spaces, (Proc. Amer. Math. Soc., 33 (1972)), 55-61 · Zbl 0249.47064 |
| [7] | Hess, P., On nonlinear mappings of monotone type homotopic to odd operators, J. Functional Analysis, 11, 138-167 (1972) · Zbl 0244.47045 |
| [8] | Kachurovskii, R. I., On Fredholm theory for nonlinear operator equations, Dokl. Akad. Nauk SSSR, 192, 969-972 (1970) · Zbl 0206.14103 |
| [9] | Krasnoselskii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations (1964), Pergamon: Pergamon Oxford · Zbl 0111.30303 |
| [10] | Lasota, A., Une généralization du premier théorème de Fredholm et ses applications à la théorie des équations différentielles ordinaires, Ann. Polon. Math., 18, 65-77 (1966) · Zbl 0139.09201 |
| [11] | Lasota, A.; Opial, Z., On thé existence and uniqueness of solutions of nonlinear functional equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 15, 797-800 (1967) · Zbl 0177.19902 |
| [12] | Leray, J.; Lions, J. L., Quelques résultats de Visik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93, 97-107 (1965) · Zbl 0132.10502 |
| [13] | Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Dunod, Gauthier-Villars: Dunod, Gauthier-Villars Paris · Zbl 0189.40603 |
| [14] | Ma, T. W., Topological degrees for set-valued compact vector fields in locally convex spaces, (Dissertationes Math., 92 (1972)), 1-43 |
| [15] | Milojević, P. S., Multivalued Mappings of \(A\)-Proper and Condensing Type and Boundary Value Problems, (Ph.D. Thesis (May 1975), Rutgers University: Rutgers University New Brunswick, N.J) · Zbl 0362.47028 |
| [16] | Milojević, P. S., Some generalizations of the first Fredholm theorem to multivalued condensing and \(A\)-proper mappings, Boll. Un. Mat. Ital., 13-B, 619-633 (1976), (5) · Zbl 0362.47028 |
| [17] | P. S. Milojević\(AA\); P. S. Milojević\(AA\) |
| [18] | Milojević, P. S.; Petryshyn, W. V., Continuation theorems and the approximation-solvability of equations involving multivalued \(A\)-proper mappings, J. Math. Anal. Appl., 60, 658-692 (1977) · Zbl 0367.47032 |
| [19] | Nečas, J., Remark on the Fredholm alternative for nonlinear operators with application to nonlinear integral equations of generalized Hammerstein type, Comment. Math. Univ. Carolinae, 13, 109-120 (1972) · Zbl 0235.47039 |
| [20] | Nečas, J., Fredholm alternative for nonlinear operators and applications to partial differential equations and integral equations, Časopis Pest. Mat., 65-71 (1972) · Zbl 0234.47050 |
| [21] | Nussbaum, R. D., The Fixed Point Index and Fixed Point Theorems for \(k\)-Set Contractions, (Doctoral Dissertation (1969), University of Chicago) · Zbl 0174.45402 |
| [22] | Nussbaum, R. D., The fixed point index for local condensing maps, Ann. Mat. Pura Appl., 89, 217-258 (1971) · Zbl 0226.47031 |
| [23] | Petryshyn, W. V., On the approximation-solvability of nonlinear equations, Math. Ann., 177, 156-164 (1968) · Zbl 0162.20301 |
| [24] | Petryshyn, W. V., Nonlinear Equations Involving Noncompact Operators, (Proc. Sympos. Pure Math., Vol. 18 (1970), Amer. Math. Soc: Amer. Math. Soc Providence, R.I), 206-233, Part I · Zbl 0232.47070 |
| [25] | Petryshyn, W. V., On projectional-solvability and the Fredholm alternative for equations involving linear \(A\)-proper operators, Arch. Rational Mech. Anal., 39, 270-284 (1968) · Zbl 0176.45902 |
| [26] | Petryshyn, W. V., Invariance of domain theorem for locally \(A\)-proper mappings and its implications, J. Functional Analysis, 5, 137-159 (1970) · Zbl 0197.40501 |
| [27] | Petryshyn, W. V., Antipodes theorem for \(A\)-proper mappings and its applications to mappings of the modified type \((S)\) or \((S)_+\) and to mappings with the pm property, J. Functional Analysis, 7, 165-211 (1971) · Zbl 0218.47029 |
| [28] | Petryshyn, W. V., Fredholm alternative for nonlinear \(A\)-proper mappings with applications to nonlinear elliptic boundary value problems, J. Functional Analysis, 18, 288-317 (1975) · Zbl 0297.47050 |
| [29] | Petryshyn, W. V., Fredholm alternative for nonlinear \(k\)-ball-contractive mappings with applications, J. Differential Equations, 17, 82-95 (1975) · Zbl 0292.47057 |
| [30] | Petryshyn, W. V., On the approximation-solvability of equations involving \(A\)-proper and pseudo-\(A\)-proper mappings, Bull. Amer. Math. Soc., 81, 223-312 (1975) · Zbl 0303.47038 |
| [31] | Petryshyn, W. V.; Fitzpatrick, P. M., A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings, Trans. Amer. Math. Soc., 194, 1-25 (1974) · Zbl 0297.47049 |
| [32] | Pohožaev, S. I., Normal solvability and nonlinear mappings in uniformly convex Banach spaces, Functional Anal. Appl., 3, 80-84 (1969) · Zbl 0191.14803 |
| [33] | Pohožaev, S. I., The solvability of nonlinear equations with odd operators, Functional Anal. Appl., 1, 66-73 (1967) · Zbl 0165.49502 |
| [34] | Sadovsky, B. N., Ultimately compact and condensing mappings, Uspehi Mat. Nauk, 27, 81-146 (1972) · Zbl 0232.47067 |
| [35] | Vainikko, G., On the convergence of collocation method for nonlinear differential equations, Z. Vycisl. Mat. i Mat. Fiz., 6, 35-42 (1966) · Zbl 0154.17301 |
| [36] | Babuška, I.; Aziz, A. K., Survey lectures on the mathematical foundations of the finite element method, (Aziz, A. K., The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (1972), Academic Press: Academic Press New York), 5-359 · Zbl 0268.65052 |
| [37] | Browder, F. E., Approximation-solvability of nonlinear functional equations in normed linear spaces, Arch. Rational Mech. Anal., 26, 33-42 (1967) · Zbl 0166.12603 |
| [38] | Milojević, P. S., A generalization of Leray-Schauder theorem and surjectivity results for multivalued A-proper and pseudo A-proper mappings, J. Nonlinear Analysis Theory, Meth. Appl., 1, 263-276 (1977) · Zbl 0362.47029 |
| [39] | Milojević, P. S., On the approximation-solvability of nonlinear equations involving differentiable mappings, (Proc. Third. Internat. Symp. on Topology and Its Applications. Proc. Third. Internat. Symp. on Topology and Its Applications, Belgrade (August 1977)), to appear · Zbl 0538.47036 |
| [40] | P. S. Milojević; P. S. Milojević |
| [41] | Toland, J. F., Global bifurcation theory via Galerkin’s method, J. Nonlinear Analysis Theory, Meth. Appl., 1, 305-317 (1977) · Zbl 0477.47036 |
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