Continuation fixed point theorems for locally convex linear topological spaces. (English) Zbl 0896.47045

The author presents some continuation principles for concentrative operators between locally convex linear topological spaces and applies these general results to a second-order boundary value problem on a semi-infinite interval. The author’s results are in connection with some results by M. Furi and P. Pera [Ann. Pol. Math. 47, 331-346 (1987; Zbl 0656.47052)], R. Precup [Prepr., Babes-Bolyai Univ., Fac. Math. Phys., Res. Semin. 1988, No. 8, 17-30 (1988; Zbl 0704.34022)] and W. Krawcewicz [“Contribution à la théorie des équations nonlinéaires dans les espaces de Banach”, Diss. Math. 273 (1988; Zbl 0677.47038)].


47H10 Fixed-point theorems
34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI


[1] Dugundji, J.; Granas, A., Fixed Point Theory, (Monografie Matematyczne (1982), PWN: PWN Warsaw) · Zbl 1025.47002
[2] Brezis, H.; Browder, F. E., Existence theorems for nonlinear integral equations of Hammerstein type, Bull. Amer. Math. Soc., 81, 73-78 (1975) · Zbl 0298.47031
[3] Corduneanu, C., Integral Equations and Applications (1990), Cambridge Univ. Press: Cambridge Univ. Press New York · Zbl 0824.45013
[4] Lakshmikantham, V.; Leela, S., Nonlinear Differential Equations in Abstract Spaces (1981), Pergamon Press: Pergamon Press Oxford · Zbl 0456.34002
[5] O’Regan, D., Theory of Singular Boundary Value Problems (1994), World Scientific Press: World Scientific Press Singapore · Zbl 0808.34022
[6] Precup, R., Nonlinear boundary value problems for infinite systems of second order functional differential equations, (Babes-Bolyai Univ. Seminar on Diff. Eqns., 8 (1988)), 17-30 · Zbl 0704.34022
[7] Furi, M.; Pera, P., A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals, Ann. Polon. Math., 47, 331-346 (1987) · Zbl 0656.47052
[8] Krawcewic, W., Contribution á la théorie des équations non linéaires dans les espaces de Banach, Diss. Math., 273 (1988)
[9] Daneš, J., Generalized concentrative mappings and their fixed points, Comment. Math. Univ. Carolinae, 11, 115-136 (1970) · Zbl 0195.14903
[10] Kelley, J., General Topology (1955), D. Van Nostrand Company: D. Van Nostrand Company Toronto · Zbl 0066.16604
[11] Daneš, J., Some fixed point theorems in metric and Banach spaces, Comment. Math. Univ. Carolinae, 12, 37-51 (1971) · Zbl 0224.47032
[12] Kothe, G., Topological Vector Spaces I (1983), Springer-Verlag: Springer-Verlag New York
[13] Engelking, R., General Topology (1989), Heldermann-Verlag: Heldermann-Verlag Berlin · Zbl 0684.54001
[14] Akhmerov, R. R.; Kamenskii, M. I.; Potapov, A. S.; Rodkina, A. E.; Sadovskii, B. N., Measures of Noncompactness and Condensing Operators (1992), Birkhäuser: Birkhäuser Basel · Zbl 0748.47045
[15] Banas, J.; Goebel, K., Measures of Noncompactness in Banach Spaces (1980), New York · Zbl 0441.47056
[16] Cristescu, R., Topological Vector Spaces (1977), Noordhoff Int. Publ: Noordhoff Int. Publ Leyden
[17] O’Regan, D., Positive solutions for a class of boundary value problems on infinite intervals, Nonlinear Diff. Eqns. Appl., 1, 203-228 (1994) · Zbl 0823.34027
[18] O’Regan, D., A fixed point theorem for condensing operators and applications to Hammerstein integral equations in Banach spaces, Computers Math. Applic., 30, 9, 39-49 (1995) · Zbl 0846.45006
[19] Potter, A., An elementary version of the Leray-Schauder theorem, Jour. London Math. Soc., 5, 414-416 (1972) · Zbl 0242.47037
[20] Treves, F., Topological Vector Spaces, Distributions and Kernels (1967), Academic Press: Academic Press New York · Zbl 0171.10402
[21] Zeidler, E., (Nonlinear Functional Analysis and its Applications, Vol. I (1986), Springer-Verlag: Springer-Verlag New York)
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