Existence, Oscillation and Eigenvalue Comparison Theorems for Two- and Three-Point Fourth Order Problems
Joseph DiGiallonardo · SIAM Journal on Mathematical Analysis · 1981
Oscillation theory has produced results for boundary value problems. We generalize some of the well-known oscillation theory of Leighton and Nehari in order to obtain existence, oscillation and eigenvalue comparison theorems in two- and three-point problems. Our method produces results in nonself-adjoint cases. In our development a certain relation emerges which is essential for oscillation results in the case of eigenfunctions and hence for existence and eigenvalue comparison. We also point out generalizations to the present development.