By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee ...By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.展开更多
A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The disconti...A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（10801001） Supported by the Natural Science Foundation of Anhui Province（1208085MA13）
文摘By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.
基金Partially Supported by a DST Research Project to RG(No.SR/FTP/MS-020/2010)
文摘A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.
