No abstract

In this paper, by making use of the coincidence degree theory of Mawhin, the existence of the nontrivial solution for the boundary value problem with RiemannStieltjes Δ-integral conditions on time scales at resonanceis established, where g(s) = 1. An example is given to illustrate the main results.

In this paper, we first present a class of first-order nonlinear impulsive integral boundary value problems on time scales. Then, using the well-known GuoKrasnoselskii fixed point theorem and Legget-Williams fixed point theorem, some criteria for the existence of at least one, two, and three positive solutions are established for the problem under consideration, respectively. Finally, examples are presented to illustrate the main results. MSC: 34B10; 34B37; 34N05.