However, the corresponding results for BVP with integral boundary conditions on time scales are still very few [19 21].
When the nonlinear term f does not depend on the first order derivative, many researchers study multipoint boundary conditions on time scales, see [11, 12, 23 26].
To the best of authors' knowledge, up to the present, there is no paper concerning the boundary value problem with integral boundary conditions on time scales.
In this paper, we consider a class of nonlinear third-order boundary value problems with integral boundary conditions on time scales.
In addition, boundary value problems with integral boundary conditions on time scales represent a very interesting and important class of problems.
However, very little work has been done to the existence of solutions for boundary value problems with integral boundary conditions on time scales.
However, to the best of our knowledge, little work has been done on the existence of positive solutions for third-order boundary value problem with integral boundary conditions on time scales.
However, to the best of our knowledge, there is no paper published on the existence of multiple positive solutions to nonlinear third-order boundary value problems with integral boundary conditions on time scales.
To the best of our knowledge, few authors have considered the synchronization of reaction-diffusion recurrent fuzzy neural networks with delays and Dirichlet boundary conditions on time scales which is a challenging and important problem in theory and application.
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 Riemann-Stieltjes Δ-integral conditions on time scales at resonance.
