In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivia...In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.展开更多
This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″...This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.展开更多
By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′...By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.展开更多
By means of nonlinear alternative of Leray-Schauder type and Schauder fixed point theorem, the existence of positive solutions to singular semi-positone nonlinear third-order differential equations are established. Th...By means of nonlinear alternative of Leray-Schauder type and Schauder fixed point theorem, the existence of positive solutions to singular semi-positone nonlinear third-order differential equations are established. The results are illustrated with an example.展开更多
The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presente...The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presented. The special case when φ(s) = |s|p-2 s,p > 1 is also considered. Our analysis is based on the nonlinear alternative of Leray-Schauder and barrier strips.展开更多
The scientific literature presents a modest amount ot evidence m the use or complementary ana al[erna- tire medicine （CAM）. On the other hand, in practice, relevant results are common. The debates among CAM practiti...The scientific literature presents a modest amount ot evidence m the use or complementary ana al[erna- tire medicine （CAM）. On the other hand, in practice, relevant results are common. The debates among CAM practitioners about the quality and execution of scientific research are important, Therefore, the aim of this review is to gather, synthesize and describe the differentiated methodological models that encompass the complexity of therapeutic interventions. The process of bringing evidence-based medicine into clinical practice in CAM is essential for the growth and strengthening of complementary medicines worldwide.展开更多
基金This work was supported by Key Academic Discipline of Zhejiang Province of China(2005)the Natural Science Foundation of Zhejiang Province of China(Y605144)the Education Department of Zhejiang Province of China(20051897).
文摘In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Y605144)
文摘This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.
文摘By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.
基金supported by Natural Science Foundation of Shandong Province (ZR2009AL014)National Natural Science Foundation of China (10871116)
文摘By means of nonlinear alternative of Leray-Schauder type and Schauder fixed point theorem, the existence of positive solutions to singular semi-positone nonlinear third-order differential equations are established. The results are illustrated with an example.
基金the National Science Function of China (19971037)
文摘The existence results for the three-point boundary value problems of second-order singular differential equation (φ(y'))' = q(x)f(x, y, y'), y(0) = A,y(η) - y(1) = (η 1)B, 0 <η < 1, are presented. The special case when φ(s) = |s|p-2 s,p > 1 is also considered. Our analysis is based on the nonlinear alternative of Leray-Schauder and barrier strips.
文摘The scientific literature presents a modest amount ot evidence m the use or complementary ana al[erna- tire medicine （CAM）. On the other hand, in practice, relevant results are common. The debates among CAM practitioners about the quality and execution of scientific research are important, Therefore, the aim of this review is to gather, synthesize and describe the differentiated methodological models that encompass the complexity of therapeutic interventions. The process of bringing evidence-based medicine into clinical practice in CAM is essential for the growth and strengthening of complementary medicines worldwide.
