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
This paper first proves the following equations△u-m￣2u+f(x,u)=0, x(R￣n,n≥3 m>0 existence of decaying positive entire solution, then emphatically, proves this solution'suniqueness.
Abstract Existence of solutions for semibounded nonlinear evolution equations is established. This gives more accurate estimate of solutions and conditions of existence are more easily validated. Our results are succe...Abstract Existence of solutions for semibounded nonlinear evolution equations is established. This gives more accurate estimate of solutions and conditions of existence are more easily validated. Our results are successfully applied to prove existence and uniqueness of solutions for some KdV type equations.展开更多
A class of piecewise smooth functions in R2 is considered. The propagation law of the Radon transform of the function is derived. The singularities inversion formula of the Radon transform is derived from the propagat...A class of piecewise smooth functions in R2 is considered. The propagation law of the Radon transform of the function is derived. The singularities inversion formula of the Radon transform is derived from the propagation law. The examples of singularities and singularities inversion of the Radon transform are given.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.
文摘This paper first proves the following equations△u-m￣2u+f(x,u)=0, x(R￣n,n≥3 m>0 existence of decaying positive entire solution, then emphatically, proves this solution'suniqueness.
基金Supported by Committee of Science and Technology (No.(2002)3002), Guizhou,China.
文摘Abstract Existence of solutions for semibounded nonlinear evolution equations is established. This gives more accurate estimate of solutions and conditions of existence are more easily validated. Our results are successfully applied to prove existence and uniqueness of solutions for some KdV type equations.
基金supported by the National Natural Science Foundation of China(No.60772041 and 61071144)
文摘A class of piecewise smooth functions in R2 is considered. The propagation law of the Radon transform of the function is derived. The singularities inversion formula of the Radon transform is derived from the propagation law. The examples of singularities and singularities inversion of the Radon transform are given.
