EXISTENCE AND BOUNDS FOR MULTIPLE SOLUTIONS OF NONLINEAR EQUATIONS

Author proves a general theorem which illustrates the method used to prove the existence of a solution, and points out that this theorem is applicable to a class of two-point boundary value problems and then shows how the results can be shaprened for a subclass of two- point boundary value problems for which the location of the maximum value of the solutions is known a priori. An example is given illustrating how the method may be applied to predict the existence of three solutions of a certain boundary value problem.