An m-point boundary value problem of Neumann type for a p-Laplacian like operator Original Research Article

Let φ and θ be two odd increasing homeomorphism from View the MathML source onto View the MathML source with φ(0)=0,θ(0)=0, and let View the MathML source be a function satisfying Caratheodoryʹs conditions. Let View the MathML source be given. We are interested in the problem of existence of solutions for the m-point boundary value problem: (φ(x′))′=f(t,x,x′),t∈(0,1), View the MathML source We note that this non-linear m-point boundary value problem is always at resonance since the associated m-point boundary value problem (φ(x′))′=0,t∈(0,1), View the MathML source has non-trivial solutions View the MathML source (an arbitrary constant). Our results are obtained by a suitable homotopy, Leray–Schauder degree properties, and a priori bounds.