The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation...The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.展开更多
We establish a Dahlberg-type perturbation theorem for second order divergence form elliptic operators with complex coefficients. In our previous paper, we showed the following result: If L_0 = div A^0(x)? + B^0(x) ...We establish a Dahlberg-type perturbation theorem for second order divergence form elliptic operators with complex coefficients. In our previous paper, we showed the following result: If L_0 = div A^0(x)? + B^0(x) · ? is a p-elliptic operator satisfying the assumptions of Theorem 1.1 then the LpDirichlet problem for the operator L_0 is solvable in the upper half-space Rn+. In this paper we prove that the Lpsolvability is stable under small perturbations of L_0. That is if L_1 is another divergence form elliptic operator with complex coefficients and the coefficients of the operators L_0 and L_1 are sufficiently close in the sense of Carleson measures, then the LpDirichlet problem for the operator L_1 is solvable for the same value of p. As a corollary we obtain a new result on Lpsolvability of the Dirichlet problem for operators of the form L = div A(x)? + B(x) · ? where the matrix A satisfies weaker Carleson condition(expressed in term of oscillation of coefficients). In particular the coefficients of A need no longer be differentiable and instead satisfy a Carleson condition that controls the oscillation of the matrix A over Whitney boxes. This result in the real case has been established by Dindoˇs,Petermichl and Pipher.展开更多
In this paper, we establish the Fekete and Szego inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach...In this paper, we establish the Fekete and Szego inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in Cn.展开更多
基金Supported by the National Nature Science Foundation of China(12101356,12101357,12071254,11771253)the National Science Foundation of Shandong Province(ZR2021QA065,ZR2020QA009,ZR2021MA047)the China Postdoctoral Science Foundation(2019M662313)。
文摘The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.
文摘We establish a Dahlberg-type perturbation theorem for second order divergence form elliptic operators with complex coefficients. In our previous paper, we showed the following result: If L_0 = div A^0(x)? + B^0(x) · ? is a p-elliptic operator satisfying the assumptions of Theorem 1.1 then the LpDirichlet problem for the operator L_0 is solvable in the upper half-space Rn+. In this paper we prove that the Lpsolvability is stable under small perturbations of L_0. That is if L_1 is another divergence form elliptic operator with complex coefficients and the coefficients of the operators L_0 and L_1 are sufficiently close in the sense of Carleson measures, then the LpDirichlet problem for the operator L_1 is solvable for the same value of p. As a corollary we obtain a new result on Lpsolvability of the Dirichlet problem for operators of the form L = div A(x)? + B(x) · ? where the matrix A satisfies weaker Carleson condition(expressed in term of oscillation of coefficients). In particular the coefficients of A need no longer be differentiable and instead satisfy a Carleson condition that controls the oscillation of the matrix A over Whitney boxes. This result in the real case has been established by Dindoˇs,Petermichl and Pipher.
基金supported by National Natural Science Foundation of China(Grant Nos.11561030,11261022 and 11471111)the Jiangxi Provincial Natural Science Foundation of China(Grant Nos.20152ACB20002 and 20161BAB201019)Natural Science Foundation of Department of Education of Jiangxi Province of China(Grant No.GJJ150301)
文摘In this paper, we establish the Fekete and Szego inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in Cn.
