Bounded positive solutions of Schrödinger equations

bounded mean oscillation of solutions of the Schrödinger and wave equations

Let u(x, t) be the solution of the Schrödinger or wave equation with L 2 initial data. We provide counterexamples to plausible conjectures involving the decay in t of the BMO norm of u(t, ·). The proofs make use of random methods, in particular, Brownian motion.

Soliton Solutions for Quasilinear Schrödinger Equations

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Positive Solutions of Positive Linear Equations

Let B be a real vector lattice and a Banach space under a semimonotonic norm. Suppose T is a linear operator on B which is positive and eventually compact, y is a positive vector, and A is a positive real. It is shown that (XI—TY1y is positive if, and only if, y is annihilated by the absolute value of any generalized eigenvector of T* associated with a strictly positive eigenvalue not less than...

Bounded Solutions of Almost Linear Volterra Equations

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. AMS Subject Classifications: 45D05, 45J05.