Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (𝑝1,…,𝑝𝑛)-Laplacian Operator

Abstract

Employing a recent three critical points theorem due to Bonanno and Marano (2010), the existence of at least three solutions for the following multipoint boundary value system −(|𝑢𝑖|𝑝𝑖−2𝑢𝑖)′=𝜆𝐹𝑢𝑖(𝑥,𝑢1,…,𝑢𝑛) in (0,1), 𝑢𝑖∑(0)=𝑚𝑗=1𝑎𝑗𝑢𝑖(𝑥𝑗), 𝑢𝑖∑(1)=𝑚𝑗=1𝑏𝑗𝑢𝑖(𝑥𝑗) for 1≤𝑖≤𝑛, is established.