A Nonlinear Boundary Value Problem of Sturm-Liouville Type for a Two Dimensional System of Ordinary Differential Equations,

In this report the authors consider the boundary value problem P sub lambda xft,x,y,lambda, ygt,x,y,lambda, A sub 1 yaA sub 2 ya0, B sub 1 ybB sub 2 yb0. xt and yt are scalar functions for t epsilon a,b, A sub 1squared A sub 2squared zero, B sub 1squared B sub 2squared zero. Values of the parameter lambda eigenvalues are sought for which there exists a nontrivial solution of P sub lambda. Two existence theorems are established and these are applied in several situations previously studied. In particular, one theorem applies to a model of a nonlinear vibrating string. Author