Triple positive pseudo-symmetric solutions to a four-point boundary value problem with p-Laplacian Original Research Article

This work deals with the existence of triple positive pseudo-symmetric solutions for the one-dimensional pp-Laplacian View the MathML source(ϕp(u′))′(t)+q(t)f(t,u(t),u′(t))=0,t∈(0,1), Turn MathJax on View the MathML sourceu(0)−βu′(ξ)=0,u(ξ)−δu′(η)=u(1)+δu′(1+ξ−η), Turn MathJax on where ϕp(s)=|s|p−2⋅s,p>1ϕp(s)=|s|p−2⋅s,p>1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive pseudo-symmetric solutions to the above boundary value problem. The interesting point is that the nonlinear term is involved with the first-order derivative explicitly.