Three positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian

Abstract

In this article, we study the multipoint boundary value problem for the one-dimensional p-Laplacian $$ (phi_p(u'))'+ q(t)f(t,u(t),u'(t))=0,quad tin (0,1), $$ subject to the boundary conditions $$ u(0)=sum_{i=1}^{m-2} a_iu(xi_i),quad u'(1)=eta u'(0). $$ Using a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f involves the first derivative of the unknown function.

Keywords

• Multipoint boundary value problem
• positive solution
• Avery-Peterson fixed point theorem
• one-dimensional p-Laplacian