A Singular Boundary Value Problem for the One-Dimensionalp-Laplacian

Abstract

AbstractThe singular boundary value problem[formula]is studied in this paper whereg(s)=|s|p−2s,p>1. The singularity may appear atu=0 and att=0 ort=1 and the functionfmay be discontinuous. The authors prove that for anyp>1 and for any positive, nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions, the above-mentioned problem has a unique solution. Also, the properties of the solution are discussed in the paper