The existence of solutions for one dimensional p-Laplace equation （φp（u′））′=f（t,u,u′） with t∈（0,1） and Фp（s）=｜s｜^p-2 s, s≠0 subjected to Neumann boundary value problem at u′（0） = 0, u′（1） = 0....The existence of solutions for one dimensional p-Laplace equation （φp（u′））′=f（t,u,u′） with t∈（0,1） and Фp（s）=｜s｜^p-2 s, s≠0 subjected to Neumann boundary value problem at u′（0） = 0, u′（1） = 0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.展开更多
In this paper, we obtain the existence of positive solutions for singular second-order Neumann boundary value problem by using the fixed point indices, the result generalizes some present results.
In this paper,we study a class of fourth-order Neumann boundary value problem(NBVP for short).By virtue of fixed point index and the spectral theory of linear operators,the existence of positive solutions is obtained ...In this paper,we study a class of fourth-order Neumann boundary value problem(NBVP for short).By virtue of fixed point index and the spectral theory of linear operators,the existence of positive solutions is obtained under the assumption that the nonlinearity satisfies sublinear or superlinear conditions,which are relevant to the first eigenvalue of the corresponding linear operator.展开更多
A semipositone singular boundary value problem(BVP for short)is discussed in this paper.By Krasnaselskii’s fixed point theorem in cones,we derive suffcient conditions,which guarantee that the semipositone BVP has at ...A semipositone singular boundary value problem(BVP for short)is discussed in this paper.By Krasnaselskii’s fixed point theorem in cones,we derive suffcient conditions,which guarantee that the semipositone BVP has at least one positive solution.展开更多
In this paper,we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions.By the fixed point index,spectral theory of the linear operators,and lower...In this paper,we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions.By the fixed point index,spectral theory of the linear operators,and lower and upper solutions method,we prove that there exists a constantλ*>0 such that forλ∈(0,λ*),NBVP has at least two positive solutions;forλ=λ*,NBVP has at least one positive solution;forλ>λ*,NBVP has no solution.展开更多
The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered.In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t)...The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered.In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t)is allowed to be singular at t=0 and t=1.展开更多
By constructing an explicit Green function and using the fixed point index theory on a cone,we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary val...By constructing an explicit Green function and using the fixed point index theory on a cone,we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem,where the nonlinear term is allowed to be nonnegative and unbounded.展开更多
In this paper,we study a nonlinear semipositone Neumann boundary value problem.Under some suitable conditions,we prove the existence and multiplicity of positive solutions to the problem,based on Krasnosel’skii’s fi...In this paper,we study a nonlinear semipositone Neumann boundary value problem.Under some suitable conditions,we prove the existence and multiplicity of positive solutions to the problem,based on Krasnosel’skii’s fixed point theorem in cones.展开更多
How to determine the earth’s external gravity field with the accuracy of O(T2)by making use of GPS data and gravity values measured on the earth’s surface is dealt with in this paper.There are two main steps:to exte...How to determine the earth’s external gravity field with the accuracy of O(T2)by making use of GPS data and gravity values measured on the earth’s surface is dealt with in this paper.There are two main steps:to extend these measured values on the earth’s surface onto the reference ellipsoid at first and then to seek for the integral solution of the external Neumann problem outside the ellipsoid.In addition,the corresponding judging criteria of accuracy to solve the GPS-gravity boundary value problem are established.The integral solution given in the paper not only contains all frequency-spectral information of the gravity field with the accuracy of O(T 2),but is also easily computed.In fact,the solution has great significance for both theory and prac-tice.展开更多
A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an a...A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.展开更多
文摘The existence of solutions for one dimensional p-Laplace equation （φp（u′））′=f（t,u,u′） with t∈（0,1） and Фp（s）=｜s｜^p-2 s, s≠0 subjected to Neumann boundary value problem at u′（0） = 0, u′（1） = 0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.
文摘In this paper, we obtain the existence of positive solutions for singular second-order Neumann boundary value problem by using the fixed point indices, the result generalizes some present results.
基金Supported by NNSF of China(No.60665001)Educational Department of Jiangxi Province(No.GJJ08358+1 种基金No.GJJ08359No.JXJG07436)
文摘In this paper,we study a class of fourth-order Neumann boundary value problem(NBVP for short).By virtue of fixed point index and the spectral theory of linear operators,the existence of positive solutions is obtained under the assumption that the nonlinearity satisfies sublinear or superlinear conditions,which are relevant to the first eigenvalue of the corresponding linear operator.
文摘A semipositone singular boundary value problem(BVP for short)is discussed in this paper.By Krasnaselskii’s fixed point theorem in cones,we derive suffcient conditions,which guarantee that the semipositone BVP has at least one positive solution.
基金Supported by NNSF of China(No.60665001)Educational Department of Jiangxi Province(No.GJJ08358,No.GJJ08359,No.JXJG07436)
文摘In this paper,we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions.By the fixed point index,spectral theory of the linear operators,and lower and upper solutions method,we prove that there exists a constantλ*>0 such that forλ∈(0,λ*),NBVP has at least two positive solutions;forλ=λ*,NBVP has at least one positive solution;forλ>λ*,NBVP has no solution.
基金Supported by National Natural Science Foundation of China(10626029,10701040,60964005,11161022)Natural Science Foundation of Jiangxi Province(2009GQS0007)Educational Department of Jiangxi Province(JJ0946,GJJ11420)
文摘The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered.In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t)is allowed to be singular at t=0 and t=1.
基金supported by the National Natural Science Foundation of China(No.10626029No.10701040)+2 种基金Natural Science Foundation of Jiangxi Province(No.2009GQS0007)Educational Department of Jiangxi Province(No.JJ0946)Jiangxi University of Finance and Economics(No.JXCDJG0813)
文摘By constructing an explicit Green function and using the fixed point index theory on a cone,we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem,where the nonlinear term is allowed to be nonnegative and unbounded.
文摘In this paper,we study a nonlinear semipositone Neumann boundary value problem.Under some suitable conditions,we prove the existence and multiplicity of positive solutions to the problem,based on Krasnosel’skii’s fixed point theorem in cones.
基金supported by Chinese Science Fund(Grant No.40374001).
文摘How to determine the earth’s external gravity field with the accuracy of O(T2)by making use of GPS data and gravity values measured on the earth’s surface is dealt with in this paper.There are two main steps:to extend these measured values on the earth’s surface onto the reference ellipsoid at first and then to seek for the integral solution of the external Neumann problem outside the ellipsoid.In addition,the corresponding judging criteria of accuracy to solve the GPS-gravity boundary value problem are established.The integral solution given in the paper not only contains all frequency-spectral information of the gravity field with the accuracy of O(T 2),but is also easily computed.In fact,the solution has great significance for both theory and prac-tice.
文摘A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.
