Abstract
In this paper, the global diffeomorphism theorem due to Zampieri was generalized. The concept of the basin of attraction is the main tool of our exposition in discussing the diffeomorphism between Banach spaces. The existence and uniqueness of a solution of the fourth order elliptic boundary value problem was proved by employing our generalized theorem. The results of this paper generalize some known theorems.MSC:35J40.
Highlights
An important problem in nonlinear analysis is to find precise conditions for a local diffeomorphism f between two Banach spaces E, F to be a global one
In, Plastock [ ] reduced the global homeomorphism problem to one of finding the conditions for a local homeomorphism to satisfy the ‘line lifting property’. This property was shown to be equivalent to a limiting condition which was designated by condition (L)
We find Zampieri’s results (Theorem . ) as a consequence of Theorem
Summary
An important problem in nonlinear analysis is to find precise conditions for a local diffeomorphism f between two Banach spaces E, F to be a global one. Was employed to prove the global diffeomorphism and the existence and uniqueness of solution of boundary value problems by some authors [ – ]. ( ) there exists a coercive function k : E → R+ which admits the directional right derivatives D+V k(x), for arbitrary x, x ∈ E, y = f (x) ∈ F, v = f (x)– (y – f (x )) and a continuous mapping h : R+ → R+ such that D+V k(x) ≤ h(k(x)) and for any r > , the maximum solution of the initial value problem r = h(r), r( ) = r is defined on [ , a) and there exists a sequence tn → a as n → ∞ such that limn→∞ r(tn) = r∗ is finite. U , u ∈ H, G where W , ∩ W , (see [ , Chapter ]) can be shown to consist of W , limits of smooth functions which vanish on the boundary
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
