This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive soluti...This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.展开更多
In this paper, by using the Leray-Schauder continuation theorem, we establish the existence and uniqueness theorems of solutions of two-point boundary value problems for 2nth-order nonlinear differential equations wit...In this paper, by using the Leray-Schauder continuation theorem, we establish the existence and uniqueness theorems of solutions of two-point boundary value problems for 2nth-order nonlinear differential equations with nonlinear growth.展开更多
This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every...This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every point. First, a G2 continuous curve is constructed in three-dimensional space. Then the curve is projected normally onto the given surface. The desired interpolation curve is just the projection curve, which can be obtained by numerieally solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit ease. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface. Numerical experiments demonstrate that it is effective and potentially useful in numerical control （NC） machining, path planning for robotic fibre placement, patterns design on surface and other industrial and research fields.展开更多
基金Research supported by the National Natural Science Foundation of China (10871116)the Natural Science Foundation of Shandong Province of China (ZR2010AM005)the Doctoral Program Foundation of Education Ministry of China (200804460001)
文摘This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.
文摘In this paper, by using the Leray-Schauder continuation theorem, we establish the existence and uniqueness theorems of solutions of two-point boundary value problems for 2nth-order nonlinear differential equations with nonlinear growth.
基金National Natural Science Foundation of China(60673026,50875130,50805075 and 50875126)
文摘This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every point. First, a G2 continuous curve is constructed in three-dimensional space. Then the curve is projected normally onto the given surface. The desired interpolation curve is just the projection curve, which can be obtained by numerieally solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit ease. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface. Numerical experiments demonstrate that it is effective and potentially useful in numerical control （NC） machining, path planning for robotic fibre placement, patterns design on surface and other industrial and research fields.
