[PDF] Top 20 A Global Description of the Positive Solutions of Sublinear Second Order Discrete Boundary Value Problems

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 671625, 15 pages doi 10 1155/2009/671625 Research Article A Global Description of the Positive Solutions of Subl[.] ... See full document

... mann boundary conditions u() = u(T) = , we show the Green’s functions of the lin- ear difference operators –  u(t – ) + Lu(t) and  u(t – ) + Ku(t), where L and K are two positive constants with K < ... See full document

... used directly in the case. On the other hand, when m-point boundary value condition 1.2 is concerned, the discussion is more difficult since the problem is nonsymmetric and the corresponding operator is ... See full document

... the global behavior of the components of nodal solutions of ...a positive answer to the above question. However, when m-point boundary value condition ... See full document

... variable positive value and has linear growth at zero and locally superlinear growth at ...of positive solutions for nonlinear differential equation boundary value problems ... See full document

... of positive solutions of second-order difference equation with nonlinear boundary value ...the global structure of positive solutions of the following ... See full document

... of positive solutions for a system of nonlinear second-order difference equations subject to multi-point boundary conditions, under some assumptions on the nonlinearities of the system ... See full document

... An outline of the work is as follows. In Sect. 2, we show global bifurcation phenomena from the trivial branch with the rightward direction near the initial point. Section 3 is devoted to showing the change of ... See full document

... periodic solutions of the second-order equation x f t, x , where f is a Carath´eodory function, by combining a new expression of Green’s function together with Dancer’s global bifurcation ... See full document

... Definition 1.1 . A positive solution of problem (1.1) and (1.2) refers to a pair (r, u), where r ≠ 0, u is a solution of (1.1) with u > 0 on T and u satisfies (1.2). Meanwhilem (r, u) is called a negative ... See full document

... ary value problems; see [–] for integer order and [–] for fractional differential ...on positive solutions for the following second-order integral BVPs are obtained ... See full document

... has only the trivial solution. In order to prove the existence of a fixed point of () we make use of the Krasnoselskii-Guo fixed point theorem on cone expansion and compression (see []). It is well known that the ... See full document

... Rabinowitz’s global bifurcation theory [[4], Theorems ...the global behavior of the component of nodal solutions emanating from u = 0 in wide classes of boundary value problems ... See full document

... Krasnoselskii’s fixed point theorem, the existence of positive solutions was obtained. To the best knowledge of the authors, no work has been done for boundary value prob- lem (.) by applying ... See full document

... of positive solutions for third-order two-point or multi-point BVPs has received considerable attention; we mention a few works: [–] and the refer- ences ...the positive solutions ... See full document

... and second authors were supported financially by the National Natural Science Foundation of China (10471075) and the State Ministry of Education Doctoral Foun- dation of China ... See full document

... above mentioned literature, we investigate the existence of positive solutions to the infinite system (1.1). Our considerations will be placed in the Banach space c consisting of all con- vergent sequences ... See full document

... triple positive differential equations, the method has not been used to study this type of second-order singular boundary value problem with general differential ...these problems ... See full document

... lower solutions to the boundary value problem should exist, but constructs the specific form of the sym- metric upper and lower ...a second-order Sturm- Liouville boundary ... See full document

... upper solutions. Wei ([15]) constructed the method of upper and lower solutions for three-point boundary value problems and gave the sufficient and necessary conditions for the ... See full document