Positive solutions for nonhomogeneous boundary value problems in Banach spaces (Q613299)

Applying Darbo's fixed point theorem, the authors establish the existence and nonexistence of fixed points of the integral equation \[ T_\lambda y(t)=\int^1_0 G(t,s)f(s,y(s))\,ds+\lambda tv, \] where \(0\leq G(t,s)\leq e\) for \((t,s)\in [0,1]\times [0,1]\). They also use their abstract results to investigate the existence rsp. nonexistence of positive solutions of second-order nonhomogeneous local and nonlocal boundary value problems in Banach spaces.