Strictly positive solutions for one-dimensional nonlinear problems involving the \(p\)-Laplacian

Authors

  • U. Kaufmann
  • I. Medri

Keywords:

elliptic one-dimensional problems, indefinite nonlinearities, p-Laplacian, strictly positive solutions

Abstract

Let \(Ω\) be a bounded open interval, and let \(p>1\) and \(q∈(0,p-1)\). Let \(m∈L^{p′}(Ω)\) and \(0≤c∈L^{∞}(Ω)\). We study existence of strictly positive solutions for elliptic problems of the form \(-(|u′|^{p-2}u′)′+c(x)u^{p-1}=m(x)u^{q}\) in \(Ω, u=0\) on \(∂Ω\). We mention that our results are new even in the case \(c≡0\). 10.1017/S0004972713000725

Published

2014-01-27

Issue

Section

Articles