Critical point approaches for second-order dynamic Sturm-Liouville boundary value problems

Economics is a direction in which there becomes visible to be many occasions for applications of time scales. The time scales approach will not only unify the standard discrete and continuous models in economics, but also, for example, authorizes for payments that reach unequally spaced points in time. We are going to study dynamic optimization problems from economics, construct a time scales model, and apply variational methods and critical point theory to obtain the existence of solutions. We derive several conditions ensuring existence of solutions of dynamic Sturm{Liouville boundary value problems. Variational methods are utilized in the proofs. We discuss the existence of at least one, three and in¯nitely many solutions for the problems under di®erent conditions on the data. Examples are also given to illustrate the main results.