On the Existence of Three Solutions for Some Classes of Two-Point Semi-linear and Quasi-linear Differential Equations

Abstract

A general theorem concerning the three critical points for some classes of coercive functionals depending on a real parameter is established, which may derive existence’s results of three solutions with various sufficient conditions for some classes of two-point semi-linear boundary value problems. Moreover, by applying known three existence theorems, we derive multiple existence results for a class of quasi-linear differential equation.