in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

this work concerns the study of existence and uniqueness to heat equation with fractional laplacian dierentiation in extended colombeau algebra.

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.

The gauge freedom in the electromagnetic potentials indicates an underdeterminacy in Maxwell’s theory. This underdeterminacy will be found in Maxwell’s (1864) original set of equations by means of Helmholtz’s (1858) decomposition theorem. Since it concerns only the longitudinal electric field, it is intimately related to charge conservation, on the one hand, and to the transversality of free el...

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.

metal—polyaniline nanocomposites such as platinum-polyaniline nanocomposite is prepared by insitu oxidative polymerization of aniline and reduction of pt+4 ions into pt nanoparticles. thepolymerization of aniline was carried out in the presence of 1(2ptcn6 [potassium hexa cyanoplatinate (iv)] as oxidizing agent. during the reaction aniline monomers undergo oxidation andform polyaniline (pant) w...

The k-th semi total point graph of a graph G, , ‎is a graph‎ obtained from G by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎In this paper‎, a formula for Laplacian polynomial of in terms of‎ characteristic and Laplacian polynomials of G is computed‎, ‎where is a connected regular graph‎.The Kirchhoff index of is also computed‎.

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...

Photocatalytic hydrogen evolution over semiconducting niobate nanosheets is synergistically improved by coexisting photochemically inactive additives of clay particles and sodium chloride without precise nanoscopic structural regulation. In addition, the Pt cocatalyst loaded on the clay particles works better than that photodeposited on the photocatalytic nanosheets.