Triple positive solutions for the one-dimensional $p$-laplacian

Abstract

We consider the boundary value problem: $ \left(\varphi_p(x'(t))\right)'+ q(t)f(t, x(t), x'(t))=0, p>1, t \in [0, 1] $, with $ x(0)=x(1)=0 $, or $ x(0)=x'(1)=0 $. Using a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is the nonlinear term $ f $ is involved with the first order derivative. An example is also included to illustrate the importance of the results obtained