Solvability for a nonlinear second-order three-point boundary value problem
Using the Leray-Schauder nonlinear alternative theory, a nonconstant solution is found under suitable new conditions for the following three-point BVP \[ u'' +f(t,u)=0,\quad 0<t<1, \quad u'(0)=0, u(1)=\alpha u(\eta), \] with \(0<\eta<1\) and \(\alpha>0\) or \(\alpha<0\). Some examples are given to illustrate the results.
second-order nonlinear ordinary differential equation
scientific article; zbMATH DE number 2093832