JournalszaaVol. 22 , No. 3DOI 10.4171/zaa/1168

A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian

  • Ravi P. Agarwal

    Texas A&M University, Kingsville, United States
  • Donal O'Regan

    National University of Ireland, Galway, Ireland
  • Haishen Lü

    The Chinese Academy of Sciences, Beijing, China
A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian cover

Abstract

This paper studies the boundary value problem

(φp(u))+q(t)(f(u)+g(u))=0(0<t<1)(\varphi_p(u'))' + q(t)(f(u) + g(u)) = 0 \qquad (0 < t < 1)
  u(0)=u(1)=0\ \ u(0) = u(1) = 0

in the case p>1p > 1. A necessary and sufficient condition for the existence of C1[0,1]C^1[0,1] positive solutions and a sufficient condition for the existence of C[0,1]C[0,1] positive solutions are presented.