Positive solutions to （n-1,1） m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.     

Positive solutions of three-point boundary value problems

In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii＇s fixed point theorem and the coincidence degree.     

Positive solutions to a singular second order three-point boundary value problem

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓＴｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｈａｓｂｅｅｎｅｓｔａｂｌｉｓｈｅｄｆｏｒａｎｏｎｌｉｎｅａｒｓｅｃｏｎｄｏｒｄｅｒｔｈｒｅｅ＿ｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｏｆｔｈｅｆｏｒｍ-ｙ″ =Ｑ(ｘ)ｆ(ｙ)　　 ( 0 <ｘ<1 ) ,ｙ( 0 ) =0 ,ｙ( 1 ) =αｙ( η) ( 1 )ｏｎｌｙｖｅｒｙｒｅｃｅｎｔｌｙｉｎ [1 ] .Ｉｔｗａｓａｓｓｕｍｅｄｔｈｅｒｅｔｈａｔ 0 <η <1 ,0 <αη <1 ,Ｑ(ｘ) ∈Ｃ( [0 ,1 ] ;Ｒ+) ,ｆ(ｙ)∈Ｃ…     

Global existence of solutions to the periodic initial value problems for two-dimensional Newton-Boussinesq equations

A class of periodic initial value problems for two-dimensional Newton- Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.