摘要
This paper considers the solvability of boundary value problems with a p-Laplacian {(φ(u^((n-1))(t)))'=q(t)f(t,u(t),…,u^((n-1))(t)),0<t<+∞,u^((i))(0)=Ai,i=0,1,…,n-3,u^((n-2))(0)-au^((n-1))(0)=B,u^((n-1))(+∞)=C.By using the methods of upper and lower solution, the schauder fixed point theorem, and the degree theory, we obtain the existence of one and triple solutions. This paper generalizes several problems due to the dependence on the p-Laplacian operator, the n-1-th derivative not only in the differential equation but also in the boundary conditions. The most interesting point is that the solutions may be unbounded.
基金
This research was supported by the National Natural Science Foundation of China(No.11601493)
by the Fundamental Research Funds for the Central Universities.
