We study the existence of non-zero positive solutions a class systems differential equations driven by fractional powers Laplacian. Our approach is based on notion fixed point index, and allows us to deal with non-local functional weights boundary conditions. present two examples shed light type functionals growth conditions that can be considered our approach.

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.

in this paper we provide‎ ‎existence results for positive solution to‎ ‎dirichlet p(t)-laplacian boundary value problems‎. ‎the sublinear and‎ ‎superlinear cases are considerd‎.