We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner...We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.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 obtai...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 ...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 l...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 constant λ* > 0 such that for λ ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > 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 va...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’...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
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We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.
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.GJJ08359 No.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 constant λ* > 0 such that for λ ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.
基金Supported by National Natural Science Foundation of China (10626029 10701040+4 种基金 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.
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.
