The generalized coincidence index — application to a boundary value problem. (English) Zbl 1090.34576

Gabor, Dorota

Arch. Math., Brno 36, Suppl., 447-460 (2000).

The paper deals with a general boundary value problem \[ u'(t)=f(t,u(t),u'(t)), \]
\[ A_1(u(0))+A_2(u(T))=\alpha (u(0)), \] which can be rewritten to the coincidence problem of the form \(L(x)= F(x)\), where \(L\) is a Fredholm operator of nonnegative index and \(F\) is not necessarily compact map. Applying a homotopy invariant called a coincidence index author establish condition for existence of solution of mentioned problem.

Reviewer: Alexandr Lomtatidze (Brno)

MSC:

34G20	Nonlinear differential equations in abstract spaces
34B15	Nonlinear boundary value problems for ordinary differential equations
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

Fredholm operator; boundary value problem in Banach space; fixed point index