In this work we introduce volume constraint problems involving the nonlocal operator $$(-\Delta )_{\delta }^{s}$$ , closely related to fractional Laplacian )^{s}$$ and depending upon a parameter $$\delta >0$$ called horizon. We study associated linear spectral behavior of these when \rightarrow 0^+$$ +\infty $$ . Through limit processes on derive convergence local as respectively, well prove so...

In this paper, we study an ill-posed, nonlinear inverse problem in heat conduction and hy-drology applications. In 2], the problem is linearized to give a linear integral equation, which is then solved by the Tikhonov method with the identity as the regularization operator. We prove in this paper that the resulting equation is well-condition and has clustered spectrum. Hence if the conjugate gr...

∆p := ∆(|∆u|p−2∆u) is the operator of fourth order, so-called the p-biharmonic (or p-bilaplacian) operator. For p = 2, the linear operator ∆2 = ∆2 = ∆ · ∆ is the iterated Laplacian that to a multiplicative positive constant appears often in the equations of Navier-Stokes as being a viscosity coefficient, and its reciprocal operator noted (∆2)−1 is the celebrated Green’s operator (see [8]). Exis...

A connected graph is called Q-controllable if its signless Laplacian eigenvalues are mutually distinct and main. Two graphs G and H are said to be Q-cospectral if they share the same signless Laplacian spectrum. In this paper, infinite families of Q-controllable graphs are constructed, by using the operator of rooted product introduced by Godsil and McKay. In the process, infinitely many non-is...

In this paper, we study a nonlinear boundary value system with p-Laplacian operator

This paper studies the Laplacian operator on a metrized graph, and its spectral theory.