Measure of noncompactness and second order differential equations with deviating argument. (English) Zbl 0885.34056
The topological transversality theorem for condensing mappings is applied to the boundary value problem with deviating argument
\[
u''(t)= f(t, u(t),u'(t), u(g_1(t)),\dots, u(g_m(t))),\tag{1}
\]
\(t\in I= [a,b]\), \(u(t)= \varphi(t)\), \(t\in[a_1,b_1]- (a, b)\), in a real Banach space \(X\) in order to obtain the existence of a solution to (1). A uniqueness result is given.
Reviewer: W.Šeda (Bratislava)
MSC:
| 34K10 | Boundary value problems for functional-differential equations |
| 34K30 | Functional-differential equations in abstract spaces |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34G20 | Nonlinear differential equations in abstract spaces |
