Let L = −∆ + V (x) be a Schrödinger operator, where ∆ is the Laplacian on R, while nonnegative potential V (x) belonging to the reverse Hölder class. We establish the boundedness of the commutators of Marcinkiewicz integrals with rough kernel associated with schrödinger operator on vanishing generalized Morrey spaces.

We consider a general form of reaction-dispersion equations with non-local dispersal and local reaction. Under some general conditions, we prove the non-existence of transition fronts, as well as some stretching properties at large time for the solutions of the Cauchy problem. These conditions are satisfied in particular when the reaction is monostable and when the dispersal operator is either ...

<abstract><p>The intention along this work is to provide analytical approaches for a degenerate parabolic equation formulated with p-Laplacian operator and heterogeneous non-Lipschitz reaction. Firstly, some results are discussed presented in relation uniqueness, existence regularity of solutions. Due the diffusivity induced by (specially when $ \nabla u = 0 $, or close zero), solut...

We study the Vladimirov–Taibleson operator, a model example of pseudo-differential operator acting on real- or complex-valued functions defined non-Archimedean local field. prove analogs classical inequalities for fractional Laplacian, counterpart Dirichlet problem including property boundary Hölder regularity solutions.

In this paper, we compute universal estimates of eigenvalues a coupled system elliptic differential equations in divergence form on bounded domain Euclidean space. As an application, show interesting case rigidity inequalities the Laplacian, more precisely, consider countable family domains Gaussian shrinking soliton that makes behavior known Laplacian invariant by first-order perturbation Lapl...

In this paper we study eigenvalue problems for hemivariational inequalities driven by the p-Laplacian differential operator. We prove the existence of positive smooth solutions for both non-resonant and resonant problems at the principal eigenvalue of the negative p-Laplacian with homogeneous Dirichlet boundary condition. We also examine problems which are near resonance both from the left and ...