Multiple solutions for second-order three-point boundary value problems with image-Laplacian operator Original Research Article

In this paper, we study the second-order three-point boundary value problem with a pp-Laplacian operator View the MathML source{(ϕp(x′(t)))′+g(x(t))=f(t,x(t),x′(t)),x(0)=0,x(ξ)=βx(1), Turn MathJax on where ϕp(s)=|s|p−2s,p>1,ξ∈(0,1),β∈(0,1)⋃(1,∞)ϕp(s)=|s|p−2s,p>1,ξ∈(0,1),β∈(0,1)⋃(1,∞). We obtain sufficient conditions for the existence of multiple solutions by applying generalized polar coordinates and the Leray–Schauder degree theorem.