Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...wh...Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].展开更多
We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u...In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.展开更多
This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential w...This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational methods.Furthermore,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as well.It is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more complicated.To overcome this difficulty,we adopt different method.展开更多
In this paper,we study a class of sublinear Kirchhoff equations:-(a+b∫R_(N)|■u|^(2)dx)+△u+V(x)u=f(x,u)in R^(N),where a,b>0,V:R^(N)→R can be sign-changing,and f:R^(N)×R→R.Under some conditions on V and f,w...In this paper,we study a class of sublinear Kirchhoff equations:-(a+b∫R_(N)|■u|^(2)dx)+△u+V(x)u=f(x,u)in R^(N),where a,b>0,V:R^(N)→R can be sign-changing,and f:R^(N)×R→R.Under some conditions on V and f,we verify that the problem possesses at least one energy solution by using variational method.展开更多
基金revised September 27,2005.Research support by Natural Science Foundation of China(10271043)
文摘Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].
基金supported by the National Natural Science Foundation of China(11171262)the Specialized Research Fund for the Doctoral Program of Higher Education (200804860048)
文摘We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
文摘Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
文摘In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.
基金Supported by the Youth Foundation of Shangqiu Institute of Technology(2018XKQ01)。
文摘This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational methods.Furthermore,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as well.It is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more complicated.To overcome this difficulty,we adopt different method.
文摘In this paper,we study a class of sublinear Kirchhoff equations:-(a+b∫R_(N)|■u|^(2)dx)+△u+V(x)u=f(x,u)in R^(N),where a,b>0,V:R^(N)→R can be sign-changing,and f:R^(N)×R→R.Under some conditions on V and f,we verify that the problem possesses at least one energy solution by using variational method.
