|
In recent years, mathematics, chemistry , physics, biology, medicine, economics, engineering , control theory , and many other scientific fields emergence of a variety of nonlinear problems, in solving these nonlinear problems in the process, gradually formed a modern analytical science in a very important branch - nonlinear Functional Analysis which includes semi- ordering method , topological methods and variational methods , etc., endless fields of technology for today's non-linear problems fruitful theoretical tools , especially when dealing with the application of the various disciplines proposed nonlinear differential equations plays an irreplaceable role in 1912 LEJBrouwer on finite dimensional space to create the concept of topological degree , 1934 , J.Leray and J . Schouder this concept extended to all continuous field of Banach spaces , and later E.Rothe, MAKrasnosel'skii, PHRabinnowitz, H.Amann, K.Deimling and so on topological degree theory , cone theory and its applications in depth research , domestic Professor Zhang Gongqing , Professor Guo Dajun , Professor Chen Wenyuan , Professor Sun Jingxian nonlinear functional analysis in many other fields have made excellent achievements [ 1-30 ] . this paper mainly discusses the following third-order Differential Equations existence of Positive Solutions circumstances : λ> 0 is a parameter , δ ∈ (0,1), η ∈ [1/2, 1) is a constant. use Kranosel'skii fixed point theorem , we will give the above boundary value problem for existence of Positive Solutions for a number of conclusions.
|