The existence of n positive solutions is studied for a class of fourth-order elastic beam equations where one end is fixed and other end is movable. Here, n is an arbitrary natural number. Our results show that the cl...The existence of n positive solutions is studied for a class of fourth-order elastic beam equations where one end is fixed and other end is movable. Here, n is an arbitrary natural number. Our results show that the class of equations may have n positive solutions provided the “heights” of the nonlinear term are appropriate on some bounded sets.展开更多
Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of the method of asymptotic analysis.
The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuo...The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.展开更多
Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface w...Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface without boundary. The idea is to use a finite number of maps fordefining the surface and the inequality of Korn's type without boundary conditions for everymap and to recast these in a general functional analysis setting about quotient spaces.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.10571085).
文摘The existence of n positive solutions is studied for a class of fourth-order elastic beam equations where one end is fixed and other end is movable. Here, n is an arbitrary natural number. Our results show that the class of equations may have n positive solutions provided the “heights” of the nonlinear term are appropriate on some bounded sets.
基金Project supported by the National Natural Science Foundation of China (No.10071024).
文摘Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of the method of asymptotic analysis.
基金supported by the National Natural Science Foundation of China under Grant Nos.10671184 and 10971203
文摘The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.
文摘Inequalities of Korn's type on a surface with boundary have been proved in many papersusing different techniques (see e.g. [4, 5, 11]). The author proves here an inequality of Korn'stype on a compact surface without boundary. The idea is to use a finite number of maps fordefining the surface and the inequality of Korn's type without boundary conditions for everymap and to recast these in a general functional analysis setting about quotient spaces.
