Chinese Annals of Mathematics

This paper deals with the mixed initial-boundary value problem of Dirichlet type for the nonlinear elastodynamic system outside a star-shaped domain. The almost global existence of solution with small initial data to this problem is proved and a lower bound for the lifespan of solutions is given.

The authors investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the results obtained are universal.

Consider a system of nonlinear wave equations

A unicity theorem concerning the total derivative for entire functions of several complex variables is proved.

The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the lower critical magnetic field H_c1 at which superconducting vortices appear is estimated. In addition, the authors locate the vortices of local minimizers, which depends on the inhomogeneous term a(x).

It is known from classical differential geometry that one can reconstruct a curve with (n-1) prescribed curvature functions, if these functions can be differentiated a certain number of times in the usual sense and if the first (n-2) functions are strictly positive. It is established here that this result still holds under the assumption that the curvature functions belong to some Sobolev spaces, by using the notion of derivative in the distributional sense. It is also shown that the mapping which associates with such prescribed curvature functions the reconstructed curve is of class .

The authors prove the space of harmonic functions with polynomial growth of a fixed rate on a complete noncompact Riemannian manifold with asymptotically nonnegative curvature is finite dimensional.

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L=[0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.

In this paper, a complete classification of arc-transitive cubic graphs of order 4p is given.

The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is non-principal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the two-fold periodic orbit and three-fold periodic orbit are also obtained.

The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H³. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss curvature. The author discusses the harmonicity of the normal Gauss map and the hyperbolic Gauss map from surface with constant Gauss curvature in H³ to S² with certain altered conformal metric. Finally, the author considers the surface whose normal Gauss map is conformal and derives a completely nonlinear differential equation of second order which graph must satisfy.