Positive solutions for Sturm-Liouville BVPs on time scales via sub-supersolution and variational methods
1 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China
2 Center of Teaching Guidance, Gansu Radio and TV University, Lanzhou, Gansu, 730000, People’s Republic of China
Boundary Value Problems 2013, 2013:123 doi:10.1186/1687-2770-2013-123Published: 13 May 2013
This paper is concerned with the existence of one and two positive solutions for the following Sturm-Liouville boundary value problem on time scales
Under a locally nonnegative assumption on the nonlinearity f and some other suitable hypotheses, positive solutions are sought by considering the corresponding truncated problem, constructing the variational framework and combining the sub-supersolution method with the mountain pass lemma.
MSC: 34B10, 34B18.