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Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear
4n-th-order differential equation
y(4n)= f( t,y,y' ,y",… ,y(4n－1) ) (a)
with the boundary conditions
g2i(y(2i) (a) ,y(2i+1) (a)) = 0,h2i(y(2i) (c) ,y(2i+1) (c)) = 0, (I= 0,1,…,2n － 1 ) (b)
where the functions f, gi and hi are continuous with certain monotone properties.
For the boundary value problems of nonlinear nth order differential equation
y(n) = f(t,y,y',y",… ,y(n－1))
many results have been given at the present time. But the existence of solutions of boundary value problem
(a), (b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the
important theorem in this paper, I.e. Existence of solutions of the boundary value problem.
Y(4n) = f(t,y,y',y",… ,y(4n－1) )
a2iy(2i) (at) + a2i+1y(2i+1) (a) = b2i ,c2iy(2O ( c ) + c2i+1y(2i+1) ( c ) = d2i, ( I = 0,1 ,…2n － 1)
has not been dealt with in previous works.