Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces
The author combines the fixed point theory, fixed point index theory and cone theory to extend some results from \textit{J. Chandra}, \textit{V. Lakshmikantham} and \textit{A. R. Mitchell} [Nonlinear Anal., Theory Methods Appl. 2, 157-168 (1978; Zbl 0385.34035)] to the two-point boundary value problem \(-x=f(t,x,x,Tx,Sx),\) \(0\leq t\leq 1\), \(ax(0)-bx(0)=x_ 0,\) \(cx(1)+dx(1)=x_ 1,\) where \(Tx(t)=\int^{t}_{0}k(t,s)x(s)ds,\) \(Sx(t)=\int^{1}_{0}h(t,s)x(s)ds.\) The existence of nonnegative solutions is investigated.
nonlinear second order integrodifferential equations
scientific article; zbMATH DE number 4198788