In recent years, many authors are greatly attached to investigation for the existence and uniqueness of solution of Duffing equations, for example, 1–11 , and so forth. Some authors 8, 11, 12 , etc. proved the existence and uniqueness of solution of Duffing equations underC2 perturbation functions and other conditions at nonresonance by employingminimax theorems. In 1986, Tersian investigated t...

2 Discussion of Kneser’s Theorem 3 2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 First Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Proving Kneser’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.1 Part 1: Existence of a Prime Decomposition . . . . . . . . . . . . . 5 2.3.2 Part 2: Uniquene...

An analog of the radiation condition is found for an abstract hyperbolic equation. When this condition holds, the uniqueness theorem for a&z&u) &(p8,u) + Au = f is valid. Here n, p, and A are some linear operators depending on t and Y. For example, Eq. 0 u = &(uoo(t, X) 8,~) &(u$~u) + q(t, x) u = f is of such a type. In what follows a, = a/a, , ai = a/axi , a, = a/a,. , x = (XI )...) xN), 1 < i...

We prove an existence and uniqueness theorem for the solution with data near the vacuum in the Hard sphere.

We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.

In this paper, we prove a Second Main Theorem for holomorphic mappings in disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic with respect to meromorphic connection) the complex projective space ℙk. This is generalization Cartan’s Theorem. As consequence, establish uniqueness theorem which intersect O(k3) many totally hypersurfaces.

We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.