Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional ( p 1 , … , p n ) -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 $-\left(\right|u_i^{\prime }{|}^{p_i-2}{u}_i^{\prime })\prime =\lambda F_{u_i}(x,u_1,\dots ,u_n)$ in $\left(\mathrm{0,1}\right)$, $u_i\left(0\right)={\sum }_{j=1}^m{a}_j{u}_i\left(x_j\right)$, $u_i\left(1\right)={\sum }_{j=1}^m{b}_j{u}_i\left(x_j\right)$ for $1\le i\le n$, is established.