Abstract
The topological transversality theorem for condensing mappings stated in [7] is used to prove some perturbation theorems: a theorem on \(\gamma\)-condensing perturbation of hyperaccretive mappings and a Browder type result on the perturbation of some bijective mappings \(\gamma\)-Lipschitz mappings. An application concerning the existence and the uniqueness of solution to a boundary value problem for nonlinear second order differential equations in Banach spaces is finally given.
Authors
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
?
Paper coordinates
R. Precup, Topological transversality, perturbation theorems and second order differential equations, Babeş-Bolyai Univ., Faculty of Math. Phys., Research Sem., Seminar on Differential Equations, 3 (1989), 149-164.
About this paper
Journal
Publisher Name
DOI
Print ISSN
Online ISSN
MR: 92i:47084
google scholar link
[1] V. Barbum Nonlinear Semigroups and Differential Equaitons in Banach Space, Noordhoof, Leyden, 1976.
[2] F.E., Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc. 73, 875-882 (1967).
[3] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
[4] J. Dugundju, A. Branas, Fixed Point Theory 1, Waesawa, 1982.
[5] A. Granas, E. Guenther, J. Lee, Nonlinear Boundary Value Problems for Ordinary Differential Equations, Dissertationes Mathematicae, CCXIV, Warsawa, 1985.
[6] W.V. Petryshyn, P.M., Fitzpatrike, A degree theory, fixed point theorems and mappings theorems for multivalued noncompact mappings, Trans. A.M.S. 194, 1-25, (1974).
[7] R. Precup, Nonlinear boundary value problems for infinite systems of second order funcitonal differential equations,“Babes-Bolyai” University, Faculty of Mathematica and Physica, Preprint nr.8, 1988, 17-30.
[8] R. Precup, Measure of noncompactness and second order differential equaitons with deviating argument, Studia Univ. Babes-Bolyai, Math. 34, 2 (1989), (to appear).
[9] I.A. Rus, Principii și aplicații ale teoriei punctului fix, Ed. Dacia, Cluj-Napoca, 1979.
[10] K. Schmittt, R. Thompson, Boundary value problems for infinite systems of second-order differential equations, J. Differential Equations 18, 277-295 (1975).
[11] J.R.L. Webb, On degree theory for multivalued mappings and applications, Bool. U.M.I (4), 2, 137-158 (1974).