Solvability of a Nonlinear Infinite Points Boundary Value Problem with Nonlinear Growth
In this paper, we use the Leray-Schauder principle to study the existence of solutions of the infi-nite points boundary value problem of the second-order ordinary differential equation {x"(t)=f(t,x(t),x'(t))+e(t),t∈(0，1) x'(0)=0,x(1)=∞∑i=1a_ix(ξ_i)where f: [0,1]×R~2→R is continuous,e∈L~1[0,1],a_i∈R,ξ_i∈(0,1)(i=1,2,…)satisfy 0＜ξ_1＜ξ_2＜…＜ξ_n＜…＜1.
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