关键词: third order boundary value problem, upper and lower solutions, Volterra type integral operator, existence and asymptotic estimates

Abstract: This paper is a continuation of Paper [1].1. A new potential ψ which is defined as the correlative potential is developed in this paper. The potential ψ is different from the classical scalar potential ψ and the vector potential A developed by Helmholtz. The new formulae of the solution of egs.▽xf=ω, ▽f=P are given in terms of ψ.2. In the time-varying electromagnetic field, two new retarded potentials, the electric type retarded correlative potential ψe and the magnetic-type retarded correlative potential ψ_m, which are distinct from the classical retarded potentials A and φ, are used to solve Maxwell equations. The new formulae of solution of Maxwell equation are given in terms of ψ and ψ_m.3. The methods for constructing a rotational field with given curl function (vorticity) is proposed.

Key words: third order boundary value problem, upper and lower solutions, Volterra type integral operator, existence and asymptotic estimates