On eigenvalue intervals of higher-order boundary value problems with a sign-changing nonlinear term

In the paper, we shall consider the boundary value problem {u^(^n^)+@la(t)f(t,u,u^',u^'',u^(^3^),...,u^(^n^-^2^))=0,n>=2,t@?(0,1),u^(^i^)(0)=0,0@?i@?n-3,@au^(^n^-^2^)(0)-@bu^(^n^-^1^)(0)=0,@cu^(^n^-^2^)(1)+@du^(^n^-^1^)(1)=0 where @l>0, @a,@b,@c and @d are constants satisfying @a, @c>0 and @b,@d>=0. Intervals of @l are determined to ensure the existence of a positive solution of the boundary value problem according to the signs of a(t) and f.