Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in ...Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.展开更多
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condit...This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.展开更多
In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.
基金Foundation item： Supported by Natural Science Foundation of China（60675022）
文摘Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.
基金Supported by the NNSF of China(10371006) Tianyuan Youth Grant of China(10626033).
文摘This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.
文摘In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.
