On the Fredholm alternative for nonlinear functional equations in Banach spaces
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- by Peter Hess PDF
- Proc. Amer. Math. Soc. 33 (1972), 55-61 Request permission
Abstract:
The well-known Fredholm alternative theorem for compact linear operators is carried over to a class of noncompact, asymptotically linear mappings of monotone type of a real reflexive Banach space into its dual. An application to a nonlinear elliptic boundary value problem is given.References
- Felix E. Browder, Existence theorems for nonlinear partial differential equations, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 1–60. MR 0269962
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Peter Hess, Nonlinear functional equations in Banach spaces and homotopy arguments, Bull. Amer. Math. Soc. 77 (1971), 211–215. MR 275245, DOI 10.1090/S0002-9904-1971-12685-X
- Peter Hess, On nonlinear mappings of monotone type homotopic to odd operators, J. Functional Analysis 11 (1972), 138–167. MR 0350525, DOI 10.1016/0022-1236(72)90084-5
- R. I. Kačurovskiĭ, On a Fredholm theory for nonlinear operator equations, Dokl. Akad. Nauk SSSR 192 (1970), 969–972 (Russian). MR 0266002
- Adriaan Cornelis Zaanen, Linear analysis. Measure and integral, Banach and Hilbert space, linear integral equations, Interscience Publishers Inc., New York; North-Holland Publishing Co., Amsterdam; P. Noordhoff N. V., Groningen, 1953. MR 0061752
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 55-61
- MSC: Primary 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0301585-9
- MathSciNet review: 0301585