A class of equations with concave operators that depend on a parameter (Q1814572)

This article deals with the generalization of classical M. A. Krasnosel'skij theorems about eigenvalues of monotone and concave operators in Banach spaces with a cone to the equation of type \(x=A(x,\lambda)\) with operators \(A(\cdot,\cdot)\) that are monotone and concave with respect to the first argument and depends on the second argument in some special way. As an example the eigenvalue problem \[ x''=f(t,x),\;x(0)=a,\;x(t_ *)=x'(t_ *)=0,\;x'(t)<0\;(0<t<t_ *) \] with unknown \(t_ *\) is considered.