One-dimensional singular problems involving the p-Laplacian and\n nonlinearities indefinite in sign

2015/06/08 by Uriel Kaufmann, Kaufmann, Uriel, Iván Medri +1
Computer Science · Engineering · Mathematics · #34B15 #34B16 #34B18 #34C25 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1506.02706

openalex publication_date 2015/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Ω be a bounded open interval, let p>1 and \γ>0, and let\nm:\Ω\→\ℝ be a function that may change sign in \Ω\n. In this article we study the existence and nonexistence of positive\nsolutions for one-dimensional singular problems of the form -( \vertν^\′ \vert ^p-2u^\′)^\′=m\( x\) u^-\γ\nin \Ω, u=0 on \∂\Ω. As a consequence we also derive\nexistence results for other related nonlinearities.\n

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