Solution sets of multivalued Sturm-Liouville problems in Banach spaces (Q1335473)

The boundary value problem \(x''\in F\{t,x,x')\), \(c_ 1 x(a)- d_ 1 x'(a)= x_ a\), \(c_ 2 x(b)- d_ 2 x'(b)= x_ b\) with \(x(t)\in X\) -- (\(X\) a Banach space) is reduced to a fixed point problem. Topological properties of sets of fixed points are applied. For \(F\) almost lower semicontinuous and with compact values it is shown that the set of solutions \(S_ F\) is a retract of \(W^{2,1}(J,X)\); if the values of \(F\) are also convex \(S_ F\) is a retract of \(C^ 1(J,X)\).