Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator Hφ = (−∆+ V )φ = −(φn+1 + φn−1 − 2φn) + Vnφn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicit...

In this paper we study intermittency for the parabolic Anderson equation ∂u/∂t = κ∆u + ξu, where u : Z d × [0, ∞) → R, κ is the diffusion constant, ∆ is the discrete Laplacian, and ξ : Z d × [0, ∞) → R is a space-time random medium. We focus on the case where ξ is γ times the random medium that is obtained by running independent simple random walks with diffusion constant ρ starting from a Pois...

The generalized coupled thermo-viscoelasticity of hollow sphere subjected to thermal symmetric shock load is presented in this paper. To overcome the infinite speed of thermal wave propagation, the Lord-Shulman theory is considered. Two coupled equations, namely, the radial equation of motion and the energy equation of a hollow sphere are obtained in dimensionless form. Resulting equations are ...

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

In this paper, we develop new methods of solving the Poincaré-Lelong equation. It is mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on (1, 1)-forms. The method is shown to be effective through obtaining better, sometimes optimal, existence results for the Poincaré-Lelong equation.

We show that bounded solutions of the quasilinear elliptic equation \(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous provided functions \(g\) and \(\textbf{F}\) in suitable Lebesgue spaces.