In this paper, weconsider the fourth order p-Laplacian beam equation (?p(u??(t)))?? = f (t, u(t), u??(t)) with integral boundary conditions u??(0) u??(1) 0, u(0)??u?(0) ?10 g1(s)u(s)ds, u(1)+?u?(1) ? 10 g2(s)u(s)ds. By using contraction mapping principle, we establish existence and uniqueness of solutions for problem. The monotony iterations is also considered. At last, some examples are presen...

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

In this paper, we consider an open tube of diameter ε > 0, on the side of which a small hole of size ε2 is pierced. The resonances of this tube correspond to the eigenvalues of the Laplacian operator with homogeneous Neumann condition on the inner surface of the tube and Dirichlet one the open parts of the tube. We show that this spectrum converges when ε goes to 0 to the spectrum of an explici...