This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2...This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.展开更多
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied....The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.展开更多
An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, ...An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.展开更多
In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boun...In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.展开更多
Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point th...Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.展开更多
In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two,...In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two, and n positive solutions to the boundary value problem. Finally we give an example.展开更多
The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonli...The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel＇skii fixed point theorems on a cone, several new results are proved.展开更多
The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In orde...The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In order to achieve this aim, existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions. In this manner, the goal of this paper is gained by applying the existence and uniqueness results mentioned above.展开更多
In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the bound...In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.展开更多
文摘This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y605144)the XNF of Zhejiang University of Media and Communications (XN080012008034)
文摘The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.
文摘An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.
文摘In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.
文摘Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
基金the National Natural Science Foundation of China(11261053)The Natural Science Foundation of Gansu Province(1308RJZA125)
文摘In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two, and n positive solutions to the boundary value problem. Finally we give an example.
基金Supported by the National Natural Science Foundation of China(11071109)
文摘The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel＇skii fixed point theorems on a cone, several new results are proved.
基金Natural Science Foundation of Fujian Province under grant No.S0650010the Foundation of the Education Department of Fujian Province (JB06098).
文摘The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In order to achieve this aim, existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions. In this manner, the goal of this paper is gained by applying the existence and uniqueness results mentioned above.
基金Supported by the National Natural Science Foundation of China(No.11126245)PHR(IHLB)Funding Project for Young and Middle-aged Backbone Teachers of Beijing Union University
文摘In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.
