Multiplicity of symmetric positive solutions for a multipoint boundary value problem with a one-dimensional image-Laplacian Original Research Article

In this paper we consider the multipoint boundary value problem 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 subject to the boundary conditions View the MathML sourceu(0)=∑i=1nμiu(ξi),u(1)=∑i=1nμiu(ηi), Turn MathJax on where View the MathML sourceϕp(s)=|s|p−2s,p>1,μi≥0,0≤∑i=1nμi<1,0<ξ1<ξ2<⋯<ξn<1/2,ξi+ηi=1,i=1,2,…,n. Applying a fixed point theorem of functional type in a cone, we study the existence of at least three symmetric positive solutions to the above boundary value problem. The interesting point is that the nonlinear term ff contains the first-order derivative explicitly.