Solutions for a generalized Woods–Saxon potential

Qualitative Properties and Existence of Solutions for a Generalized Fisher-like Equation

This paper is devoted to the study of an eigenvalue second order differential equation, supplied with homogenous Dirichlet conditions and set on the real line. In the linear case, the equation arises in the study of a reaction-diffusion system involved in disease propagation throughout a given population. Under some relations upon the real parameters and coefficients, we present some existence ...

Generalized Minimizer Solutions for Equations with the p-Laplacian and a Potential Term

Let Ω be a domain in R (possibly unbounded), N ≥ 2, 1 < p <∞, and let V ∈ Lloc(Ω). Consider the energy functional QV on C∞ c (Ω) and its Gâteaux derivative QV , respectively, given by QV (u) def = 1 p ∫ Ω (|∇u| + V |u|) dx, QV (u) = div(|∇u|p−2∇u) + V |u|p−2u, for u ∈ C∞ c (Ω). Assume that QV > 0 on C∞ c (Ω) \ {0} and QV does not have a ground state (in the sense of Pinchover and Tintarev [13, ...

Se p 20 07 Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential ∗

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential V = g 2 2 (x − 1)(x + a). The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter a are discussed. PACS: 11.10.Ef, 03.65.Ge ∗Work supported in part by the U.S....

Institute for Mathematical Physics Semilinear Geometric Optics for Generalized Solutions Semilinear Geometric Optics for Generalized Solutions

This paper is devoted to the study of nonlinear geometric optics in Colombeau algebras of generalized functions in the case of Cauchy problems for semilinear hyperbolic systems in one space variable. Extending classical results, we establish a generalized variant of nonlinear geometric optics. As an application, a nonlinear superposition principle is obtained when distributional initial data ar...

Exact solutions for the flow of a generalized second grade due to a Longitudinal quadratic time-dependent shear stress