A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numeri...A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solu- tions of the nonlinear second-order ODE are investigated us- ing finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order non- linear ODE is shown to converge faster than a finite differ- ence formulation of the standard form of the second-order nonlinear ODE. Both finite difference schemes satisfy the von Neumann stability criteria. When mapping the numeri- cal solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line. A nonlinear relationship between the position of the contact line and physical parameters is obtained.展开更多
In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and wave-type equation with singular behavior...In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and wave-type equation with singular behavior at x = 0. The advantage of this single global method employed to present a reliable framework is utilized to overcome the singularity behavior at the point x = 0 for both models. The method is demonstrated for a variety of problems in one and higher dimensional spaces where approximate-exact solutions are obtained. The results obtained in all cases show the reliability and the efficiency of this method.展开更多
In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation ...In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.展开更多
By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp...By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.展开更多
Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous ...Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.展开更多
In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate ...In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes).展开更多
文摘A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solu- tions of the nonlinear second-order ODE are investigated us- ing finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order non- linear ODE is shown to converge faster than a finite differ- ence formulation of the standard form of the second-order nonlinear ODE. Both finite difference schemes satisfy the von Neumann stability criteria. When mapping the numeri- cal solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line. A nonlinear relationship between the position of the contact line and physical parameters is obtained.
文摘In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and wave-type equation with singular behavior at x = 0. The advantage of this single global method employed to present a reliable framework is utilized to overcome the singularity behavior at the point x = 0 for both models. The method is demonstrated for a variety of problems in one and higher dimensional spaces where approximate-exact solutions are obtained. The results obtained in all cases show the reliability and the efficiency of this method.
文摘In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.
基金This work was supported by the Foundation of First Period of Key Basic Research sponsored by the Department of Science and Technology of China(Grant No.2003CCA02400)National Natural Science Foundation of China(Grant No.10471029)by Natural Science Foundation of Guangdong Province(Grant No.04300034).
文摘By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.
文摘Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.
基金The Project Supported NSF of Guangdong (990444) NSFC (10071014).
文摘In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes).
