In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the bou...In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the boundary value is . First, we establish the comparison principle by the double variables method based on the viscosity solutions theory for the general equation in. We propose two different conditions for the right hand side and get the comparison principle results under different conditions by making different perturbations. Then, we obtain the uniqueness of the viscosity solution to the Dirichlet boundary value problem by the comparison principle. Moreover, we establish the local Lipschitz continuity of the viscosity solution.展开更多
Examines a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions; Proof of the comparison and maximum principles; Approximation of the finite element; Introduction...Examines a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions; Proof of the comparison and maximum principles; Approximation of the finite element; Introduction of a discrete analogue of the maximum principle for linear elements.展开更多
The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sido...The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.展开更多
In this paper, for a semi-linear parabolic partial differential equations with impulsive effects, the existence-comparison theorem and comparison principles are established using the method of upper and lower solution...In this paper, for a semi-linear parabolic partial differential equations with impulsive effects, the existence-comparison theorem and comparison principles are established using the method of upper and lower solutions. These results are applied to obtain the stability results of the steady-state solutions in a reaction-diffusion equations modelling two competing species with instantaneous stocking.展开更多
文摘In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the boundary value is . First, we establish the comparison principle by the double variables method based on the viscosity solutions theory for the general equation in. We propose two different conditions for the right hand side and get the comparison principle results under different conditions by making different perturbations. Then, we obtain the uniqueness of the viscosity solution to the Dirichlet boundary value problem by the comparison principle. Moreover, we establish the local Lipschitz continuity of the viscosity solution.
基金This paper was supported by the common Czech-US cooperative research project of the programmeKONTACT No. ME 148 (1998).
文摘Examines a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions; Proof of the comparison and maximum principles; Approximation of the finite element; Introduction of a discrete analogue of the maximum principle for linear elements.
文摘The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.
基金Supported by the National Natural Science Foundation of China(No.10071048).
文摘In this paper, for a semi-linear parabolic partial differential equations with impulsive effects, the existence-comparison theorem and comparison principles are established using the method of upper and lower solutions. These results are applied to obtain the stability results of the steady-state solutions in a reaction-diffusion equations modelling two competing species with instantaneous stocking.
