## 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).