Abstract In this work, we consider the solvability of a fractional-order p -Laplacian boundary value problem on half-line where fractional differential operator is nonlinear and has kernel dimension equal to two. Due nonlinearity operator, Ge Ren extension Mawhin’s coincidence degree theory applied obtain existence results for at resonance. Two examples are used validate established results.

Let (M, g) be a compact Riemannian manifold of dimension ≥ 3. We show that there is a metrics g̃ conformal to g and of volume 1 such that the first positive eigenvalue the conformal Laplacian with respect to g̃ is arbitrarily large. A similar statement is proven for the first positive eigenvalue of the Dirac operator on a spin manifold of dimension ≥ 2.

This paper describes a fast corner detection algorithm making use of the Laplacian of Gaussian operator. We propose a general corner model and analyze its behavior in scale space. The study shows that the response of the operator has a stable elliptic extremum which always lies inside the corner. Using a multi-scale representation limited to two scales and the sole laplacian of Gaussian operato...

Convergence to a single steady state is shown for non-negative and radially symmetric solutions to a diffusive Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions, the diffusion being the p-Laplacian operator, p ≥ 2, and the source term a power of the norm of the gradient of u. As a first step, the radially symmetric and non-increasing stationary solutions are characterized.

In this work we propose a generalization of the Heat Kernel Signature (HKS). The HKS is a point signature derived from the heat kernel of the Laplace-Beltrami operator of a surface. In the theory of exterior calculus on a Riemannian manifold, the Laplace-Beltrami operator of a surface is a special case of the Hodge Laplacian which acts on r-forms, i. e. the Hodge Laplacian on 0-forms (functions...