In this article,we will prove that,under the differential condition,the strict pseudo_convexity and Orgega_Rheinbold pseudo_convex are equivalent.What's more,we will discuss the relation between the r_convexity an...In this article,we will prove that,under the differential condition,the strict pseudo_convexity and Orgega_Rheinbold pseudo_convex are equivalent.What's more,we will discuss the relation between the r_convexity and the analog convexity.展开更多
The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity...The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.展开更多
The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean curvature.Furthermore,a second order partial differential equati...The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean curvature.Furthermore,a second order partial differential equation for the Gauss map is obtained,and it is shown that this equation is the complete integrability condition of the representation.展开更多
文摘In this article,we will prove that,under the differential condition,the strict pseudo_convexity and Orgega_Rheinbold pseudo_convex are equivalent.What's more,we will discuss the relation between the r_convexity and the analog convexity.
基金supported by the National Natural Science Foundation of China(No.11201292)Shanghai Natural Science Foundation(No.12ZR1444300)the Key Discipline"Applied Mathematics"of Shanghai Second Polytechnic University(No.XXKZD1304)
文摘The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.
基金supported by the National Natural Science Foundation of China (Nos. 10571068,10871149)the Research Fund for the Doctoral Program of Higher Education (No. 200804860046)
文摘The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean curvature.Furthermore,a second order partial differential equation for the Gauss map is obtained,and it is shown that this equation is the complete integrability condition of the representation.
