The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,...In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,is established under certain conditions of convexity.展开更多
This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance pri...This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.展开更多
Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It ...Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .展开更多
文摘The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
基金supported by the National Natural Science Foundation of China under Grant No. 10871098the Natural Science Fund of Jiangsu Province under Grant No. BK2009397the Innovation Fund of Youth of Fujian Province under Grant No. 2009J05003 and CNPq Brazil
文摘In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,is established under certain conditions of convexity.
基金supported by the National Natural Science Fundation of China under Grant No.60874006
文摘This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.
基金supported by the National Natural Science Foundation of China(Nos.11201119,11471099)the International Cultivation of Henan Advanced Talents and the Research Foundation of Henan University(No.yqpy20140043)
文摘Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .
