Monotone positive solutions for p-Laplacian equations with sign changing coefficients and multi-point boundary conditions

Abstract

We prove the existence of three monotone positive solutions for the second-order multi-point boundary value problem, with sign changing coefficients, $$displaylines{ [p(t)phi(x'(t))]'+f(t,x(t),x'(t))=0,quad tin (0,1),cr x'(0)=-sum_{i=1}^la _ix'(xi_i)+sum_{i=l+1}^ma_ix'(xi_i),cr x(1)+eta x'(1)=sum_{i=1}^kb_ix(xi_i)-sum_{i=k+1}^mb_ix(xi_i) -sum_{i=1}^mc_ix'(xi_i). }$$ To obtain these results, we use a fixed point theorem for cones in Banach spaces. Also we present an example that illustrates the main results.

Keywords

• Second order differential equation
• positive solution
• multi-point boundary value problem